I prefer to reverse into a bay for all the reasons given above, and also because the way steering geometry works, the car is more maneuverable in reverse so it's easier to get into a tight space. The car park nearest our supermarket has a pavement down one side, so if I can get into one of the bays on that side there's actually footpath access to the back of the vehicle, so nice and easy.
Otherwise I just park the trolley at the front of the car and take a carrier bag in each hand round to the boot...repeat until the trolley is empty.
There's a store near me that when it was built, had a footpath between two rows of parent and child spaces, so that if you reversed in you had footpath access to the boot. But people didn't use it, they preferred to drive in, then when they came out of the shop park their trolley and pushchair at the back of the car...where there's moving traffic...and yell at anyone who dared drive within ten feet of their pushchair.