Hello, I know it’s best for baby to sleep in bassinet in the same room for at least 6 months. My baby is 3 months and can already roll. It seems that the bassinet is now too small for him and he wakes up a lot due to not having room. Would you recommend we just keep him in the bassinet or move him to his room with his cot? Thanks

Most babies will be rolling over by 4- 5 months. 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 his new environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over

Continue to place him on his back for sleep.
How does he go with tummy time when awake?
Increase tummy time when awake to aid building of upper body strength which also assists rolling well.

Yes, Room Sharing for first 6 months is recommended. That can be in a cot or a bassinet(prior to rolling).
He does need to be moved to his cot now that he is rolling. (see article in above link)
Once babies are rolling, they need the space of a cot & arms free (no swaddling/wrapping) to roll well.
Will the cot fit in your room?

See link to info about room sharing,(esp 1st paragraph) including the following:

” Parents are not expected to observe their baby constantly. If your baby is sleeping in a separate room check baby regularly to ensure that the baby remains on the back and the head and face remain uncovered “

” The protective effect of room sharing can be partially explained by increased adult supervision and observation of the baby “
https://rednose.org.au/article/room-sharing-with-baby