How to handle letting kitten out my room situation?

I have a 9 month kitten for about 6 now.i have to keep her in my bedroom because my moms is scared of kittens.my mom has a phobia of animals.scared of all of them,even my turtle.only thing my mom aint afraid of is fish.my kitten is happy though,she plays around often,has a lot of toys to play with,jumps on my dresser,bed,computer etc.
My kitten nevers tries to run out the room.even if i leave the door wide open she wont try to run out or meow or anything.she would just sit there.my mom said i can let her out to play in the living room in the evening from 7pm till whateva time i go 2 bed.my mom dont come in the living room at that time,
my question is how do i handle this situation?if i let her out that time every evening will she try to run out the room everytime i open the door?how do i handle this

I would just open the door and talk to her, and let her decide when to come out and how far she wants to come. It might take some days before she makes the decision. Talk to her and praise her a lot.