The way the rules are written (and were intended to be interpretted
) was the following:
The attacker flies his air units into a territory. After the attacker has moved, the defender flies defensive air support.
The side with the least number of fighters deploys his planes first (or the defender if equal) as either air-to-air or as bombers. Then the other player does the same. Then the side with the least number of fighters (or the defender if equal) decides how many of his air-to air fighters are going to be by-passing interceptors (and go after bombers) then the other player does the same.
Then air to air combat is resolved, players may choose to take their air-to air casualties off of air to air fighter or by passing interceptor fighters (but by-passing interceptors don't get to shoot back in air-to-air combat). Then interceptor to bomber combat is resolved. Surviving bombers then get to strategically attack.
So, your attacking fighter is not "locked" into a bombing role until after you set up the planes per the steps above. The attacking fighter could be deployed as an air-to-air fighter if the attacker wishes.