The BOM is generally best used against ground forces.
Using a BOM for SBR is a nearly 17% chance per run of losing a $15 BOM in order to do an average $3.5 of damage. Over many games, that will average out to a slight boost in terms of economic trade to the nation doing the SBR. But the risk of loss of the BOM against AA fire is high.
Using a BOM for land combat, when adequately protected by ground units, is a MUCH better trade.
If you have enough ground forces, and are not attacking AA protected territories, your risk to your BOM is minuscule (total dice fracks being the only real risk, and you can still retreat once your ground fodder is gone to avoid minor dice fracks)
Used for ground combat, the BOM will do $6 of damage to your opponent (2 dead INF) per 3 rounds of combat. It will shorten battles by killing defenders faster (preserving your own units).
SBR MAY be the best use of a BOM if you get a free-roll (no AA gun present) against an opponent, but even then it depends on how beneficial the BOM would be in other combat being conducted that round (You are probably better off bringing the BOM to a battle that will go 2 or more turns than you are using it even for a free SBR). There are of course exceptions, but the above is a good general rule.
Finally, even on rounds when teh BOM is not needed for combat, I still think twice about doing an SBR against an AA protected target. Sure, the BOM may not have anything to do THIS turn, but what about next turn, or 3 turns from now? If I send it on SBR, I have a 1 in 6 chance to lose it, and then it will not be available for later attacks.