For the flexibility the car offers I would take it.
You should certainly visit Iona.
Assuming good weather head for Calgary Bay for a picnic lunch. Or get geared up and climb Ben More.
Definitely visit Fionnphort and spend some time soaking up the ancient ecclesiastical atmosphere on Iona. Take the Staffa boat tour. Preferably book to avoid disappointment.
Hit Tobermory distillery. Not too hard, obviously.
Thanks so very much....especially good advice about the distillery :)
If you have got a full day on Mull it's a good idea to take the car and see more of the island. You won't have time to visit all the places mentioned by Rudyard, but you can do some of them. Iona would be my choice.
Whilst it is possible to get around Mull by bus, it takes a lot of meticulous planning, so you can fit what you want to see in with the bus timings. There are buses, but not overly regular, even in Summer. Not impossible but a pain. The car will give you way more flexibility.