...would you want me giving my number out?"

Was talking to this chick at the club and things were going well, so I went for the number and got the, "I've got a BF routine." I pretty much ignored it and kept going and got it again -the whole time she is smiling with non-stop eye contact and we were barely inches apart. IOI's all over the place. Second time I said we could all go hang out together and hold hands or some shit. She was kind of startled, but I just kept going.

The place was closing and we walked out together and I went in again and this time she stopped and said the above line. I wasn't really sure what to say here so I said something like, "Well, if you did then you weren't very serious about me to begin with, blah blah blah." It was all pretty lighthearted, but I got nothing.

Better response?

This sounds like a shit test and your answer failed it, IMO

Things you could have done/said include shrugging your shoulder or ask her for her number again and completely ignore what she said.

You could have said:

"If WE were going out?! wow don't get ahead of yourself you haven't even taken me out for a drink yet"

or if you had a banter together and have an inside joke this would be a perfect time to bring it up.

I agree completely.
Hahaha, that's perfect! Thanks.