My 3.5 month old has started rolling back to tummy (can’t go tummy to back). We know she needs to go into a cot but we don’t have space in our room. Is it better to be in a bassinet in our room or a cot in a different room?

Red Nose recommendations are to “always place baby on back for sleep” not baby must always sleep on their back.
https://rednose.org.au/article/red-nose-safe-sleeping-recommendations

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 the “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?
Increasing tummy time when awake is important to build upper body strength to roll well (both ways)
Is she rolling from tummy to back during tummy time, holding her head well &/or reaching for toys?

You are correct, it is important for your baby to be sleeping in a cot now & to cease swaddling/wrapping.
Many parents are unable to room share for all sleeps..
Some parents find a portable cot (that meets Mandatory Standards) is helpful to continue room sharing till 6 mths.
Ensure doors are open & you are able to hear her, & when you wake up during the night, check on her.
No parent is expected to sit up all night/day watching baby.

Important to maintain all of the rest of the safe sleep recommendations, in particular:
  always place baby on back,
  keep head & face uncovered (nothing loose or soft in the cot)
  provide the safe environment (cot with firm, flat(not elevated) mattress.