It is possible for a bomber to shoot down the fighter in an interception, but only if the fighter has at least 50% damage when the interception happens.
The combat during an interception works via rounds the same as any other combat in the game with the main difference being that there is an upper limit to the number of rounds of combat that can happen (5 in unmoded BtS) which is why both units can survive without there being a withdrawal chance. The odds of winning each round is proportional to the units' air strength values. Given that an undamaged BtS Bomber has an air strength of 16 and the undamaged fighter has a 12 the bomber has a 16*100/(16+12) percent chance of winning each round, which is actually 57% (since it is rounded down). That makes it look like the bomber should win the fight more than the fighter. But that does not take into account the amount of damage that is inflicted when a round is won. The damage inflicted is calculated as a defined value, MAX_INTERCEPTION_DAMAGE which is normally set to 50, scaled by the unit's current interception chance. A fighter has an interception chance of 100 so it will inflict 50 points of damage when it wins if it is undamaged. A Bomber has an interception chance of 0 so it looks like it will not do any damage, but there is also a defined MIN_INTERCEPTION_DAMAGE which is set to 10 so a bomber will do 10. At this point it is important to note that a unit's interception chance scales with the damage it has taken - if the fighter has taken half damage then it will have half the interception chance and also do half as much damage when it wins a round.
So with an undamaged bomber (no promotions) vs an undamaged fighter (no promotions) the bomber will win, on average, 57% of the combat rounds with up to 5 rounds before the fight ends. It only takes the fighter 2 hits, gotten by winning 2 rounds, to shoot down the bomber but it would take the bomber 10 hits to shoot down the fighter (which is not possible because there are only 5 rounds). That 57% chance per round for the bomber means the fighter often takes some damage and it is also why it is possible for the bomber to survive - it has to win at least 4 of the 5 rounds of combat to do so, working out to about a 28.7% chance of surviving. There is about a 6% chance that the bomber will win all 5 rounds and take no damage itself while causing the fighter 50 points of damage.
An undamaged bomber vs. a half damaged fighter is the point where it becomes possible for the bomber to shoot down the fighter - even a single hit point more than half left for the fighter means it can't happen. If neither unit has any promotions, the bomber now wins 16*100/(16+6) = 72% of the combat rounds (since the air combat strength of a unit scales directly with damage, the half damaged fighter is only strength 6 instead of 12). It now will take the fighter 4 hits to shoot down the bomber (as it will cause 25 points of damage per win) and it will take the bomber 5 hits to shoot down the fighter. If I did the math right, there is about a 98% chance that the bomber will survive and about a 20% chance that it will shoot the fighter down. (And there was only a 50% chance that the fight would even happen, the other 50% of the time the bomber is not intercepted and gets to perform its assigned mission.)
There is a condition in the code that does allow a bomber to get experience without shooting down the intercepting fighter. It is the condition where both units survive and not only did the bomber survive but it took no damage, which requires winning all 5 combat rounds when the fighter has at least 51 hit points at the start. That has about a 6% chance of that happening for the usual no damage no promotions example. When it does happen, the bomber gets the number of XP specified by the EXPERIENCE_FROM_WITHDRAWL setting, which is 1 for BtS. If both units survive but the bomber takes damage, then the fighters gets this experience unless the fighter took no damage (which can only happen if the fighter started out damaged badly enough that it can't destroy the bomber even when it wins all 5 rounds, but the odds of it winning all 5 when it is so badly damaged are very low - I expect this is in there for ground units that can intercept since they never take any damage when intercepting so they will always trigger this exception).
All this is why you should clear the way with fighters first. Assuming equal promotions, it's pretty much a 50-50 fight for 2 undamaged unpromoted fighters. There is no chance that both will survive since they each need 2 hits to destroy the other and there is no way for that to not happen when the round limit is set to 5 (it would have to be way down at 2 for this to be possible). So either you eliminate a defending fighter (with a 50% chance of your fighter being undamaged and a 50% chance of being half damaged) or you don't but have a 50% chance the defender is at half damage. That is a lot better than the roughly 71.3% chance that an undamaged unpromoted fighter will shoot down an undamaged unpromoted bomber (and a 100% chance that it will intercept, preventing the bomber from doing what it was trying to do). Starting by sending in cheaper unit with a better survival chance = a good plan.
Some of the odds calculations might be slightly off, but I think this is all correct. Probably.