Not convinced that hand shuffling a deck is random

Although I don't shuffle track, I find myself believing that hand shuffling doesn't randomize the cards very well. For example, in 1 deck there's a Ace of Hearts on top of the pile. You then do a bridge shuffle mixing in the bottom and top halves together. Then you do a regular shuffle which just reverses the other of the cards. The algorithm is always the same. It's always either reversing the decks order or just mixing bottom and top cards which doesn't do anything profound. Anybody see what I'm saying? Probably not. I just have obcessive compulsive disorder or something.