There's a woman in my field who I know of, we have a Twitter 'relationship' and I'd imagine she knows my work even if she doesn't know it's mine IYSWIM. Helps that I know she interviewed to be the head of my department and was offered but turned it downs
I want to approach to her to ask her to be a mentor of sorts. Not so formal but she's done really well in her career and I'm surrounded by blokes, so it would be nice to have someone who understands what it takes to get ahead in our world.
Can I cold email/DM her? I know on paper it seems normal but part of me feels I'm being cheeky for essentially asking her to give me her time/expertise/knowledge for nothing in return?