Driving in Barbados is fine, nothing to worry about at all. Bajans are generally kind drivers, willing to let you out of side roads etc. even if they have priority. A smile and a wave will get you far.

Things I would recommend are:
1) Sat-nav. Essential, especially if you're going to be on the east coast where signposting is not particularly clear.

2) Get a large car with a decent amount of power. Some of the hills inland are very steep and smaller hatchbacks struggle to get up the steepest ones.

3) Mind the potholes. Some are deceptively deep, especially on some of the remote roads which aren't used very often.