Bedford Ma Cheap Apartments For Rent . 17 apartments available for rent in bedford, ma. On rentcafe, new bedford, ma rents go as low as $630/mo. 2/3 Bedroom Apartment Mansfield NG19 in Mansfield, Nottinghamshire from www.gumtree.com Town of bedford, 10 mudge way bedford, ma. As of february 2022, the average apartment rent in new bedford, ma is $826 for a studio, $1,175 for one bedroom, $1,601 for two bedrooms, and $1,776 for three bedrooms. Finding a home nearby is easier than you think.