Hello,
Welcome to the ehealthforum and I am really glad to help you out. Your concern is regarding the removal of mole on head. First of all, a mole should be removed only if it is suspicious looking or suspicion of a melanoma is there.
Since you have burnt scalp after being out in the sun and also the bump bleeds on touch, so it is advisable to get a biopsy of the bump done as if it is a melanoma or a skin malignancy then it is better to identify it early.
I sincerely hope that helps. Take care.