Need to stop thinking about her so much, should i tell her we should stop talking awhile?

I cant stop thinking about my ex girlfriend. Im still very much in love with her. she has a new boyfriend. we lost our virginities to each other which makes me think about her and miss her so much more. I do need to move on cuz shes made it clear that we wont be together again as a couple, but she doesnt want me out of her life for good. We have kept in consistent contact, and lately she has been sort of ignoring my messages. not completely, she will answer them after 4 or more hours but it irritates me. so should i jsut tell her its best for me probably to stop talking to her so i can get over her easier? all i think about right now is her with the other guy kissing and being happy. and i do want her to be happy, but still sucks. so im pretty sure i should just tell her i need to stop talking to her if she is just oging to be ignoring me like she has been, i do want to be friends with her, but not as a doormat for her. but if anyone else has advice what i need to do, or say to her, then ill appreciate it.