How can I make my 'best friend' either date me or stop doing this?

There is nothing you can do to change other people but change yourself. She probably likes but she does not wants to date. Don't try to convince her to go out with you. Have a talk with her and tell you are not comfortable with the situation. You don't want to be on HOLD until she makes a decision. At this time the best thing is keep away from her. If she really likes she will be force to do something about. There are billion of girl that would like to go with you. You will no be able to fall for another girl until you try to go with others. I know because I went through an experience like that and I get tire of waiting suddenly I started liking someone else and because I still thinking about of the other one I lost the other guy. It's your life and you have to make a decision, don't let her make a decision for you. Congratulation dear for not taking advance of while she was drunk. That tell me how a nice guy you are. There a million girl that would like to go out with you. May God bless and guide you to the right direction.