Your hand here has massive equity against pretty much anything. When raised on the flop I would just keep putting money in the pot and just ship it. You also block the nuts which is helpful. As played if you get to river this way I think bluffing is very reasonable. I wouldn't expect to see many Ax in villain's range that take a raise flop line. The main one would be AJ but I would also expect that to bet turn. I'd bet river for like ~85c.

I agree with @Komododragonjesus. I think that you should've played a little less timid given the high equity of your hand.

Playing a 12 out draw so slowly here and not trying to leverage any fold equity shows that you're not fully up to speed with equities in a fairly standard spot. It's vital that you download a program such as Equilab, and play around with flop textures like this one to build up your understanding of how well you're doing.

With so many outs to basically the nuts, if the money goes in on the flop you're actually ahead of hands like AJ and QQ. Even if he has JJ you will still win more than 40% of the time. Factor in any fold equity you have against weak made hands andyou can see shoving the flop is super profitable compared to being so passive.