My 4 month old sleeps arms out in a sleeping bag on her back in a bassinet with mesh sides. No matter if I position her in the middle or to the right hand side, she's managing to wriggle to the left and has her face pressed up against the mesh. Moved her several times but still wiggles back and it's giving me major anxiety, is this safe? I put her in the cot for a nap and she did the exact same thing in that.

There is no need to stop your baby from wriggling & changing her position, but it is important to continue to make her environment safe.
Many babies will wriggle & change position (like you describe) at a younger age. This is very normal.
The next step will most likely be rolling.

How does she go with tummy time?
Are you still wrapping her?
It is not unusual for baby to be rolling at 4 months.

Most babies will be rolling over by 4-5 months…....some earlier, some later.
Often, they start by wriggling & changing position as you have described.
This is very normal as babies grow & become stronger when many then prefer to sleep on their tummy &/or side.

*It is important that you move her from bassinet to his cot now & cease swaddling.
*Baby needs arms free & the space of the cot to roll safely.

Once she is rolling it is important to make the environment as safe as possible for this to occur.
Continue to place baby on the back to sleep.
Ensure cot mattress is firm, well-fitting & flat.
Ensure there is nothing loose or soft in the cot.
Preferable to use a sleeping bag when rolling that has appropriate size neck & arm holes.

Red Nose has the following information when baby is rolling.
Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

*Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.com.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over