When to ask her out?

This girl ive known and liked for around 3 months went off me around a month ago for being too desperate with asking her out (her reason was she didnt know me well enough). recently i got back in touch with her and i said i wanted to start again through a text. i met her at her work last weekend for a couple of hours and conversed with banter and laughs like before with her and her friend (build more face to face comfort). i plan to do the same next weekend. Would the weekend following that be too much in seeing her again though? dont want too seem desperate. i intend to ask her for a walk on the beach after she finishes work the weekend after that weekend lol. On the whole is a month slow enough before asking her out? if she rejects me after that i would be surprised because the obvious signs of interest are there but also clueless as to what to do next.
do you think she would accept this time? to be fair before i was asking her out virtually every weekend for 4 weeks.

thanks,

If she rejected you four times already, I'd say give up and move along. It is *very* unlikely that she will have changed her mind.

Saying she won't go on a date because she doesn't know you well enough frequently is just a nice way of saying she doesn't want to. The whole point of a date is to get to know you.