I plan on asking my gf to stay off of her phone while we are in bed together.
What is the reason why it bothers you when she is on her phone in bed.
It's sure she's talking to other men
While you want to be careful not to control everything that your girlfriend does, it is also important that you two be present with one another in the time you have. If you simply want your girlfriend to be present in bed with you, kindly asking her to do this for that reason should work just fine. If it doesnt, then you have the right to be upset.
I just want to spend more time with her too.
It is ok to want to spend more time with your girlfriend. You should probably talk to her about this and see if she is ok with putting her phone down at the end of the day while in bed. This may be a great time for you guys to catch up and find out how one another's days were.