Our 10 week old is starting to roll, she rolls from tummy to back on her own during tummy time and can roll back to side in her bassinet, but so far mostly favours sleeping on her back, though does often move to her side through the night. For this reason we have changed her to arms free sleeping. Should we be putting her in the cot now or can we wait until she is sitting up? My concern is her cot is on the other side of the house and cannot fit in our room so I’m not sure what’s safer, keeping her in the bassinet with us or having her in her own room?

Most babies will be rolling over by 4- 5 months. Some earlier, some later.
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side or tummy.
This is not something that needs to be stopped. It is important to make her new environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

How does she go with tummy time when awake?
Increase her tummy time when awake - more frequently if she is not tolerating long periods on her tummy.
Increased tummy time when awake helps to build upper body strength to assist with rolling both ways.
As she is rolling we would recommend you transfer her to cot now &, as you have done cease swaddling/wrapping.
Babies need arms free & the space of a cot to roll well.
Ensure the cot mattress is firm & that there is no loose/soft bedding.

Still, always place her on her back for sleep.

Can her cot be placed closer to your room? Or do you have a portacot you could use for a couple of months in your room?
Room sharing is about supervision, so if she is not in the room with you, we would recommend regular checking when you wake up during the night