which do you consider your "true" rating: blitz, std, bullet, online?

My ratings range from 1500 (blitz) to 1730 (online). I also have a rating of 1700 in bullet but that's due to the fact that I was lucky during the few games of bullet I played. Which is my true rating? Is it my blitz rating given that I've by far played more blitz games than I have any other type of chess game? Or is it my online rating given that I had enough time to decide my moves and never ran out of time?

They are all "true" ratings.  Each is representative of your performance in the pool in which it was generated.

I suppose that's true, but I don't consider my bullet rating of 1700 to be accurate. I just got lucky. By that logic we could argue that my blitz rating must be a more accurate rating given that I've played over a thousand blitz games, but then again, how many times I outplayed my opponent but ran out of time? I could say that my online rating is more accurate since time management problems did not come into play, but then again, in no official chess tournament are players allowed to spend up to a day per move or use an analysis board.

But time management is an important skill in blitz, so I'd say the fact that time management problems come into play for you, leading to a lower rating due to losses on time, just means that your blitz rating is perfectly indicative of your blitz performance.  Losses on time are still losses, and if you feel that's the leading reason for your worse performance in blitz then I'd say you've got a good handle on what you need to work on if you want to improve your blitz game.

Rating is simply a measure of performance, so the idea that it can be "inaccurate" is an indication of a misunderstanding of this point.  It is not really a predictor of future performance -- simply a measure of past performance that's often (mis)used as a predictor of the future.  As a result, the inaccuracy is not in its calculation, but rather its use.

Longer time controls are more indicative of your real skill. So, something like 30/30 (which is pretty fast) would tell you less about how good you are than a 60/60. 

I'd consider a FIDE rating a true rating.  None of the games here at chess.com are very similar to true OTB play in a tournament situation.

Outside of that, the ratings here are a reasonable representation of how well you do in that particular area against that pool of opponents.  As long as you don't assume it means anything in the real world, it does the job it's designed to do.