I'd suggest giving Bomber Starships minor damage bonuses against Structural, Ultra-Heavy, Command-Grade etc.
That would work, and would reinforce their similar role to bomber fleetships.
However, as you mentioned, the bonus should be minor. Their unboosted DPS is already pretty good, even by star-ship standards.
If we want to get crazy, the unboosted DPS can go down a good chunk and make it allowed to hit non-large stuff (though favoring large stuff, like the plasma siege starship now), but I kind of like the role they got now. It just needs a bit of a buff to do its role well enough to be worth it.