asking out dilemma!!!!

hey,
theres this girl i like and weve known each other for little over two months now. ive visited her a few times where she works locally from me with her friend to build face to face comfort and avoid too many text conversations. She rejected me a while ago because i came across as too desperate and rushed into things, she said at the time she didnt really know me. Our contact is still good so im presuming she's still interested but just wants me to be more relaxed and take it slower (not in friend zone because of flirting signs), which is what im doing. fact is ive considered asking her if she wants to hang out alone with a walk on the beach, but not to ask this through texting. ive had past experience of rejection through this and i'd rather ask her face to face. Although this conveys i have a form of interest in her i do not plan to start a relationship at this time (hence the 'hang out' and not 'asking out,' i can only hope she understands that) i like this girl and i do want a relationship at some point but after stepping back and realising that id only seen her a couple of times in 5 weeks at one point a while back made me think she had a point. Problem is her friend is there the whole time constantly, i dont want to ask it infront of her friend because it seems like im pressuring her, and i will be humiliated if she says no also as she might not be ready. i want to talk to her face to face and get to know her better personally without her friend there. what should i do?

any help much appreciated!!