I had the same problem with my toddler when we switched babysitters. At first I pushed her to go "bond" with the new babysitter but the harder I pushed, the more resistant my daughter became. So I changed strategies and stopped asking the babysitter to look after my daughter at all. Instead, I let my daughter stay near me (as she wanted) and let her see that the babysitter and I were developing a nice relationship. After a couple of weeks, my daughter seemed to notice that the babysitter was actually a very nice person! So then she WANTED to spend time with her. I think she needed the chance to stand back and observe rather than be pushed into a relationship - which is probably what we all need.

I agree that patience and not pushing can be helpful. But I also think you can tell your little girl that she has to speak more nicely to the babysitter. Like Sarah Chana says, "all feelings are acceptable but not all BEHAVIORS are acceptable." Even if she's not ready to go with the babysitter, she shouldn't be allowed to say unkind things!