How does maintenance differ for military fighters/bombers vs. commercial airliners?
I think a few things need to be examined here:

1) The type of flying.  A commercial aircraft is closer to a military C-17 than a B-52 or F-16 in how it is used.  It has several stops throughout the day for loading and unloading.  The maintenance in between stops does not need to be very extensive - because it has just landed, presumably working fine, the things that need to be checked primarily involve what has the most chance of decaying during a flight (tires, oil, general wear and tear, etc).  Fighters/bombers don't generally fly several legs in a day.  Fighters might double/triple turn, and in between each of these flights the maintenance inspection is a much lower requirement than between each day of flying.

2) Component Requirements.  Supersonic jet engines need maintenance more often than high bypass commercial engines.  They are stressed much more, and work on a much tighter margin of error, thus fighter/bomber aircraft need maintenance more often.

3) Age.  Military fighter/bomber aircraft are on average much older than the average commercial aircraft.  B-52's are from the 50's, and B-1's are from the 80's (along with most of the fighter fleet).  Older aircraft require more maintenance, and there is no avoiding it.

Between fighters and bombers, they each have different flying styles.  Fighter engines work a lot harder than bomber engines (except the B-1, which essentially has the same engine as an F-16), and thus require maintenance more often.  Bombers are much larger, and have more systems that can break.  

Hope this helps.

Update: Incorporating a suggestion from the comments below, it is probably useful to specifically mention a few more specific maintenance items unique to combat aircraft

1) Ejection Seats:  Most military combat aircraft carry ejection seats, which have a very specific maintenance routine.  This may include repacking the associated parachute, and checking to ensure that all components are functional/in good repair.

2) Weapons:  The obvious difference between fighters/bombers and commercial airliners is that they carry weapons.  This means that there is a software package that needs to be maintained (that controls the weapons), the aircraft hardware needs to be maintained (ie bomb bays, missile racks, hard points, etc), and the weapon itself requires building/deconstruction.

3) Flight Computer:  Combat aircraft often have tactically specific functions in their flight computer that a commercial airliner would not.  There are routines to help calculate bomb trajectory, to link with other combat aircraft and many other military specific tasks that a commercial airliner would not need.

I would agree with an earlier statement stating that performance has a slightly higher emphasis than reliability in military aircraft than in commercial aircraft.  It's easy to see how the requirement to carry bombs/missiles increases aircraft gross weight, which lowers fuel efficiency.  Every internal bomb bay could potentially be a fuel tank extending range.  Hard points, even when bombs aren't installed, cause drag lowering performance.  In the end, designers have to determine which capability is more important - endurance, payload, power, etc.  You may want to install a triply redundant INS in a fighter aircraft, but you're adding weight that decreases performance, and taking space which could be devoted to other avionics (like radar).