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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.
 
Have you researched "Nuclear Modified Flying Bomb" in the Rocket tech tree? That is required to load nukes on any sort of rocket.