Many bus routes pass through Long Melford. Probably the most useful ones for the visitor connect to the village from Sudbury, Bury St Edmunds, Colchester, Ipswich and Haverhill.
There are also several other routes through the surrounding villages, but some of them run on only one or two days in the week.
To get full details on the bus services around Long Melford the best source is the East Anglia Traveline web site. If you hit the link for 'Plan a Journey', it will allow you to put in your starting and ending points, and the time when you want to travel, and then responds with details of the services available, including a change on the way if necessary.