Our brand new baby (6 days old) is currently sleeping in a bassinet. We've had a couple of instance where we've come in and he's been sleeping on his side even though we placed him on his back. This was the position that he was in in the womb - so perhaps he likes it. We aren't sure what to do about this. Do we move him back each time he does this? Do we need to wake up throughout the night to check on this?

Most babies do not roll to tummy intentionally before 3 months; however, some babies do roll, especially to the side, at a very early age.

What type of bassinet are you using?
Some babies do not respond well to wrapping/swaddling & prefer to have their arms free.         
Are you wrapping him?
Some babies like to touch their face or suck fingers when settling.
You could try settling him without any swaddle, or wrap with his arms out.

Have you commenced tummy time yet when awake?
https://rednose.org.au/article/tummy-time-is-good-for-baby-because
Always place baby on the back for sleep.
You could also consider moving him to a cot.

You are not expected to wake during the night to keep checking on him.
However, there is nothing wrong with rolling him back if you see him on his side.

Red Nose does not recommend the use of sleep positioners.
Red Nose does not recommend positional products such as anti-roll devices and items that fasten a baby into a sleeping position.
Products that restrict the movement of a baby or a baby’s head should not be used.
https://rednose.org.au/article/is-it-safe-to-use-products-designed-to-keep-baby-in-a-particular-position