Red Nose advises that you should move baby from a bassinet to a cot when they show signs of being able to roll. Why? If my bassinet has high sides made of taut, breathable mesh, will this suffice until baby is able to reach the top rim of the bassinet (i.e. until they can sit or stand)?

The reason for moving baby from the cot when they look like rolling is to allow them the space to move & roll safely.
It is difficult for baby to move, once rolling, if they do not have their arms free (no swaddling/wrapping) or have limited space (ie in a bassinet)
Rolling is a normal development stage which can start as early as 3mths - occasionally before that.
Most babies will be rolling between 4-5mths.

This is the general information in relation to the rolling question.

Most babies will be rolling over by 4- 5 months…...some earlier, some later.                             
This is normal as babies grow & become stronger.
Many babies then prefer to sleep on their tummy or side.
This is not something that needs to be stopped. It is important to make the environment as safe as possible.

Have a read of the Red Nose information when baby is rolling . 
Cease swaddling & move from bassinet to cot.

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).
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.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over