Costco – Bristol – Opening Hours & Store Details You will find Costco situated at an ideal location on St Brendan’s Way, about a 5.49 mile drive north-west from the centre of Bristol, in Avonmouth (a few minutes walk from Royal Mail Avonmouth Delivery Office). This store is delighted to serve customers within the areas of Cabot Park, Shirehampton, Easton In Gordano, Lawrence Weston, Bristol City Centre, Pill, Rushpool and Avonmouth. Here you will find some pertinent information about Costco Bristol, including the hours of business, location particulars and direct contact number.