Stockport Bus Station is a terminus for about 65 bus services in the Greater Manchester area. It is just over Wellington Road from Mersey Square.
From Mersey Square walk straight through Merseyway Shopping Centre and turn right. You can can get to the Old Town area through Chestergate, Little Underbanks or Bridge Street Brow.
There are also bus stops on Wellington Road near the library. Turn right at the library down St Petersgate and walk right along it to the Old Town.
Alternatively there is a free shuttlebus which you can jump on at the bus station. This runs every 12 minutes, from 10.30am to 5.30pm on a Sunday.