For $2US ($1US each way) you can take a scenic bus ride from Bridgetown to Welchman Hall Gully. The journey takes about 30 to 45 minutes. DO NOT BUY TOKENS. These are for the blue government buses only. Cash only $1US each way or $2BDs each way.
You need to get to Cheapside bus terminal. Super easy if you are coming from the west coast or from the cruise ship terminal. From the west coast, any bus going into Bridgetown, ends at Cheapside. From the port it is about a 10 minute walk. Just ask anyone and they will point you in the direction. It is very safe to walk.
For the south coast, it is a bit more tricky. All the buses end in the main bus terminal which is on the other side of the Bridgetown. It is a 15 plus minute walk, again just ask for directions. Barbadians are very friendly and helpful.