I don't think it is rude.
In many European countries restaurant bills are paid in such a manner that the waiter/waitress knows how much tip he/she receives. I like that much better. That way there is that moment when the waitperson can thank you personally for the tip, which I think is nice. If I give a good tip, I like to see the person to which I gave it being happy.
Well however you pay it, the waitperson picking up the bill is not rude. People prepare food for you, bring it to you and you pay for it. Get over it; why the secrecy?