I'm going to ask my girlfriend to stop texting me
Why do you want your girlfriend to stop texting you?
I'm busy and I don't need her distractions
Just tell her you will respond to her later. You don't have to tell her to stop texting.
It is really getting on my nerves.
Just be nicer to her in this situation. Tell her you are busy instead of saying don't text me. It sounds more sensitive.