In all essence thats a good idea. Let slip that you should get to know each other better or whatever and if you are getting the "im not interested that way" vibes then just put it down to the booze.
BUT DONT GET TOO SHITFACED.
To be fair I'm sure birds dont actually think that if you do ask them out. If anything they are flattered.
You feel a right tit because you feel you have embarassed yourself in reality you havent.
Unless of course you were completely drunk and were making an ACTUAL tit of yourself.
Plus...