Did the Soviet military in fact fear that the Space Shuttle would be used as an orbital bomber? If so, why?

We know the Soviets feared the shuttle. In response they developed their own: Buran programme, for, among other goals:

carrying out military-applied research and experiments to ensure the creation of large space systems using weapons on known and new physical principles (ru:WP)

But it was really just to stay on-par or not get too much behind. The logic for it is quite sound, on first glance. The response time for such an attack is cut quite short compared to ICBMs launched from US soil. But the achieved realities are of cause fraught with problems, like those mentioned in the question.

Unlike Nasa, Soviet developers never had any grand illusions about replacing traditional rockets with a reusable space truck.
Instead, the Soviet shuttle was conceived primarily as a "symmetrical response" to the perceived military threat from America's winged orbiters.

Albeit with quite delusional rumours being spread by officials. Rumours about the American shuttle that couldn't be taken seriously by anyone who ever saw this falling brick in a landing approach:

Years after a sceptical Pentagon had given up on the shuttle, even as a delivery truck for spy satellites, the Russian officials continued whispering to journalists that the US orbiter had a secret capability - to make an undetected "dive" into the Earth's atmosphere and suddenly glide over Moscow dropping nuclear bombs.
Never mind that such a scenario was not supported by physics or by common sense.
Energia-Buran's chief architect, Valentin Glushko, hardly tried to educate warmongers at the Politburo about the questionable merits of the re-usable orbiter as a weapon.
_{Anatoly Zak: "Buran - the Soviet 'space shuttle'", BBC News, 20 November 2008}

It was ultimately fuelled by fears stemming from the Nazi-German origins of both space programmes. The Germans brought with them the hitlerite vision of an antipodal bomber (like Silbervogel), crossing half the globe to drop a load and then return in one go.

This is even somewhat reflected in the continuity of names given to the programmes, from pure bomb delivery to Soviet shuttle:

Since Korolyov's OKB-1 was too heavily preoccupied with its R-7 ICBM, responsibility for the cruise missiles was entrusted to the aviation industry by a government decree released on 20 May 1954. Three aviation design bureaus were tapped to build cruise missiles with different missions:

OKB-49 (Georgiy Beriyev): a missile called Burevestnik ("Petrel") or "P-100" to be used for long-range reconnaissance (fulfilling the same role as the American U-2 reconnaissance aircraft) and also to deliver small 1.2-ton nuclear warheads.
OKB-301 (Semyon Lavochkin): a missile called Burya ("Storm") or La-350 to transport 2.18-ton atomic bombs.
OKB-23 (Vladimir Myasishchev): a missile called Buran ("Blizzard") or M-40 to transport 3.4-ton hydrogen bombs.

And the Soviet fear of American capabilities is equally rooted in their own design goals for such vehicles:

In 1958–1959 OKB-52 began working on two projects called Kosmoplan and Raketoplan. Raketoplan was initially conceived as a suborbital vehicle to carry passengers and cargo over intercontinental distances and, more importantly, to perform bombing missions.

A study often cited with respect to the origins of the Soviet shuttle program was performed at the Academy of Sciences' Institute of Applied Mathematics (IPM). Headed since 1953 by Mstislav Keldysh (President of the Academy of Sciences from 1961 to 1975), this institute had been involved in mission modeling and ballistics computations since the early days of the space program. The IPM studies were conducted under the leadership of Yuriy Sikharulidze and Dmitriy Okhotsimskiy, two of its leading scientists.

The IPM studies focused on the Shuttle's possible use as a bomber, more particularly its capability to launch a nuclear first strike against the United States. Efraim Akin, one of the institute's scientists, later recalled:

"When the US Shuttle was announced we started investigating the logic of that approach. Very early our calculations showed that the cost figures being used by NASA were unrealistic. It would be better to use a series of expendable launch vehicles. Then, when we learned of the decision to build a Shuttle launch facility at Vandenberg for military purposes, we noted that the trajectories from Vandenberg allowed an overflight of the main centers of the USSR on the first orbit. So our hypothesis was that the development of the Shuttle was mainly for military purposes. Because of our suspicion and distrust we decided to replicate the Shuttle without a full understanding of its mission.

When we analysed the trajectories from Vandenberg we saw that it was possible for any military payload to re-enter from orbit in three and a half minutes to the main centers of the USSR, a much shorter time than [a submarine-launched ballistic missile] could make possible (ten minutes from oI the coast). You might feel that this is ridiculous but you must understand how our leadership, provided with that information, would react. Scientists have a different psychology than the military. The military, very sensitive to the variety of possible means of delivering the first strike, suspecting that a first-strike capability might be the Vandenberg Shuttle's objective, and knowing that a first strike would be decisive in a war, responded predictably''

The report produced by the IPM scientists has never been made public, leaving unanswered many questions about the technical details of such a mission. Apparently, the Russians believed the Shuttle could drop bombs on Soviet territory while re-entering from a single-orbit mission from Vandenberg or by briefly "diving" into the atmosphere and then returning to orbit. As Energiya–Buran chief designer Boris Gubanov writes in his memoirs:

"The studies … showed that the Space Shuttle could carry out a return maneuver from a half or single orbit …, approach Moscow and Leningrad from the south, and then, performing … a "dive", drop in this region a nuclear charge, and in combination with other means paralyze the military command system of the Soviet Union."

What lent this scenario particular credibility from the Russians' perspective was the Shuttle's 2,000 km cross-range capability, demanded by the Air Force to enable the Shuttle to return to Vandenberg after a single orbit around the Earth. However, such single-orbit missions from Vandenberg were not considered for a nuclear strike against the Soviet Union, but to quickly service polar-orbiting US spy satellites or even pluck enemy satellites from orbit, barely giving the Russians a chance to detect such operations with their space-tracking means [16]. Leaving aside the question whether such missions were feasible, the capability to return to Vandenberg after a single revolution was needed anyway to allow the Shuttle to perform a so-called "Abort Once Around" in case it ended up in an unacceptably low orbit after a main engine failure.

One can only guess what led the Russians to believe that the Shuttle had a nuclear first-strike capability. Possibly, they were "inspired" by their own plans for a so called Fractional Orbit Bombardment System, an orbital nuclear weapons system designed to attack the US via the South Pole rather than passing through the net of radar systems at the northern approach corridor. The Soviet Union worked on three such systems in the 1960s, one of which (using Yangel's R-36 missile) actually reached operational status by the end of the decade.

Even though it bordered on paranoia, IPM's assessment of the Shuttle's first-strike capability is said by many to have been a decisive factor in convincing the Soviet leadership of the need to build an equivalent system (although a more rational reaction would probably have been to upgrade anti-missile defense systems). Gubanov writes:

"On the basis of the results of the analysis, M.V. Keldysh sent a report to the Central Committee of the Communist Party, as a result of which L.I. Brezhnev, actively supported by D.F. Ustinov, took the decision to work out a set of alternative measures to guarantee the safety of the country."

However, new evidence shows that Keldysh put his signature under the IPM report on 26 March 1976, which was more than a month after the official party and government decree that sanctioned the Soviet shuttle program. Still, it cannot be ruled out that the studies began well before that time and that preliminary results did play some role in the Soviet decision to move forward with a Space Shuttle equivalent.

_{Bart Hendrickx & Bert Vis: "Energiya-Buran: The Soviet Space Shuttle", Springer Praxis: Berlin, Chichester, 2007. (emphasis added)}

One note to concerns in the question: "Needed highly trained astronauts to fly". –– The details were not fully known to the Soviets in the early stages. And the Soviets designed their Buran to be able to fly fully automated!