Have you researched and built strategic bombers? I've never had a problems with Abombs when I used strats.
You need to click on the individual bomber division to get the load icon. So if you have a group of 2 or more strat bombers, you don't see an option to load the A bombs until you get down to division level where you see the unit stats and the disband option.
I think somelse said that you first need to build or use a nuke on a strat bomber before you can do it on an ICBM. Since B29s were used to drop the only A bombs used in WW2, that seems o.k. to me. Do the historic thing first then do the new thing.