If the offers provided by buses do not suit your needs, trains and carpooling could represent a good alternative for this distance.
Since the journey from Dudley to Bristol is not so long, the bus is a good solution, but if you are looking for more offers or departure times, you can also have a look at trains and carpooling solutions.
When are the buses of the line Dudley - Bristol scheduled?
To get to Bristol from Dudley by bus, it will take you around 4 hours and 26 minutes, or even 3 hours and 25 minutes if you choose the fastest solutions. The first bus leaves Dudley at 05:02, while the last one is at 19:02.
By bus from Dudley to Bristol: which companies offer the service?
There are many companies cooperating with virail, among which also National Express with buses to Bristol.