While you're at it make sure the name of your business on the card is printed out as "Female Body Inspector" and make sure you have the capital letters big in bold while all the other letters are way smaller lol
Just like JackZero said it does seem a little cowardly because it is
There are so many other ways and better ways to do this, but if you really don't have time to talk to her then you should say to her that you are both very busy there and you have enjoyed talking with her. Then TELL her she "should" give you her number so you can talk more when you both have some time.
This gives a great and valid reason as well... the lack of time.
I would wait and see what her reaction is when you say the first thing about enjoying talking with her because if she isn't enjoying it and doesn't agree and sound enthused then that could be a sign to let it go lol
Best luck man.