I've gone over the Manhattan Bridge many times on a Citibike. It isn't so bad. You're not going to be passing anybody except someone on another Citibike that is even slower than you are.

I'll use it once or twice a week once the weather gets better, usually to ride downtown after work. It is actually the fastest way for me to get home, ride a Citibike down 2nd Ave to the Grand St. station and take the subway the rest of the way to Brooklyn. Neither the 2nd Ave bus nor the downtown 6 train can beat it. I never go the other way though. Too much hassle to get off the subway and find a bike, only to be somewhat sweaty when I get to the office. If I want to ride in the morning I take my own bike the entire way.