Noooooooo!! Don't ask for a date.
The maybe next time was most likely a polite way to say no you can't have my number. Then you gave her yours, and if my first assumption was right I don't think she has any intention of using it.
She knows you are interested and isn't showing interest back. Do not pursue her any further.
'People are never perfect but love can be. People waste time looking for the perfect lover rather than creating the perfect love' - Princess Leigh-Cheri from Still Life With Woodpecker.