My opinion is that playing pre-moves in bullet isn't a dirty tactic and shouldn't annoy you. It's a legitimate and necessary way to play in order to save time. Saying that, you have to be smart about how and when you pre-move, and your occasional strategy of exploiting a pre-move with something bad which wins a piece if the reply is automatic is also a perfectly legitimate tactic. Anything goes in bullet.
Deliberate Blunders in Bullet Chess.

Works sometimes. Other times it'll just get you a quick loss.
The tougher bullet players are usually expecting this kind of stuff, though, so the higher up the ranks you climb, the less often it works.

Do I find falling for these tricks frustrating ? Yes. Is it within your right ? Yes. Is it bad sports ? This is a bullet game.
The only thing I disagree with in your logic is the fact that premoves are unsportsmanly. They are part of the game, but tricks like yours are the risks that have to be taken when premoving.
Often times in bullet games players tend to pre-move in the early game in an attempt to gain a slight time advantage later on. I'll be honest, this really annoys me. As a result I started to respond by playing deliberate inaccuracies(and occasionally genuine blunders) when I believed a player was pre-moving. A common example of this can be found in the attached game below.
The fact that this (and similar) tactics succeeded in a minority of games (maybe 30-35%) didn't really surprise me. What did was the abuse that followed once I'd taken the opposition queen. I expected to be called an idiot etc etc because many chess players are rude. What I didn't expect was for some players to have an issue not with losing but with what I'd done. In my mind I legitimately countered a dirty tactic (stealing early seconds), in theirs I was the one playing dirty. I see nothing wrong with exploiting typical pre-moving errors, but I'm curious as the the opinion of others.