Bobbi is a super-spy who used to work for SHIELD. I don't think she'd have much difficulty finding Peter Parker's phone number. He's probably in the phone book (well, phone directory -- I don't think many places publish physical phone books anymore).
Plus she has contacts for various other people in Peter's life from her time as both his bodyguard and his girlfriend (Aunt May, for example) so she could get his number through one of them if needed. She also knows his secret identity and they have various superhero friends and teammates in common, which is another method for her to get in touch with him.
Even IF Mockingbird were unable to reach Peter for some reason, she knows plenty of other tech experts who could assist her. Tony Stark is the most prominent example. She is also the adviser to G.I.R.L., who have a few genius-level engineers. Plus she may have a few tech experts working for her W.C.A. (World Counter-terrorism Agency) who could also help her.
I don't think Mockingbird has any problems with keeping her wings working.