Is dropping a bomb an action and do you drop the bomb and move or move then drop the bomb?

Each bomb drops in the way that it says it drops on the upgrade card.

Didn't answer the first part. Is it considered an action.

Bombs can only be dropped when specified on the individual bomb cards. So far, the only bomb that is dropped with an action is Proximity Mines. What I think you're asking, though it's not clear, is if a ship is given a free action, can it drop a bomb? So given the above the only time the answer would be yes is with Proximity Mines. (Though off the top of my head, I can't think of anything Imperial that would allow you to do that, since right now only Imperial craft can carry/drop bombs.)

Proximity mines are actions but the other 2 aren't. You drop them as part of the manuer step.

Bombs can only be dropped when specified on the individual bomb cards. So far, the only bomb that is dropped with an action is Proximity Mines. What I think you're asking, though it's not clear, is if a ship is given a free action, can it drop a bomb? So given the above the only time the answer would be yes is with Proximity Mines. (Though off the top of my head, I can't think of anything Imperial that would allow you to do that, since right now only Imperial craft can carry/drop bombs.)

Squad Leader allows that.

The full rules for using bombs are in the latest FAQ and normally come with any ship capable of using them, namely the Slave I and the TIE Bomber.