I am not a lawyer so I'm not standing behind this entirely. You need to do your own homework. But you transcription is your work. You cannot claim to have written the solo as that would be plagiarism but if you transcribe the music you are generating your own work. You just have to give credit where credit is due, proper notation of who wrote and performed the work.
You cannot copy other peoples transcripts and pass them around as that violate copyright law. Many musicians and music teachers write their own copies of music from scratch to avoid this. I do not know if they are firm ground but I haven't heard any bad news. It is always a good idea to ask.
If you do not know who to ask you can look up on Harry Fox Agency website. HFA issue recording rights, not transcription rights, but they also have contact info for legal representation of the people who hold the aritist's work. Asking never hurts.