By bus
National Express (http://www.nationalexpress.com) operate services to Marlborough St Coach station, located in the city centre, from cities throughout the UK including London. The journey from London to Bristol takes about 2h30min. Tickets are much cheaper if booked in advance online.
Megabus (http://uk.megabus.com) also operate budget coach services from London Victoria coach station to a stop outside the Colston Hall in Colston Street Behind Flavourz restuartant formerly Yates Winelodge City Centre or UWE. Tickets must be booked online and fares are demand responsive but can be very cheap £1.50 if you book far enough in advance. The journey to London takes about 30 min longer than by National Express.
By train
Wikitravel has a guide to Rail travel in the United Kingdom.
Bristol Temple Meads station is located approximately 15 minutes walk from the city centre and has regular inter-city and regional train services from Bath, Birmingham, Cardiff, Edinburgh, Exeter, Glasgow, London, Plymouth, Southampton, Swansea and York. It is the oldest, continuously and still operating train station in the world. Today, it is run by the train operating company First Great Western, who provide the majority of services.
Bristol has a second main railway station in Bristol Parkway, which is located several miles north of the city centre. Although this station also has frequent services to many of the same locations as Temple Meads, it is principally aimed at suburban residents and is unlikely to be useful to visitors.
From London, you can travel from London Paddington station. There are several through trains an hour, the fastest of which takes one hour and ten minutes. Train times from any location can be found on the National Rail Planner (http://www.nationalrail.c...) or by calling 0845 748 4950 from anywhere in the UK.Alternatively, there is Megatrain , a budget train service running out of London Waterloo to Bristol Temple Meads, with one or two trains a day taking just over two and a half hours.
By car
The M5 and M4 motorways intersect near Bristol and the M32, a motorway 'spur', brings traffic directly into the city centre. The M4 links London with Bristol with a driving time of less than two hours.
The city also has 3 Park and Ride facilities, A4 Portway, Long Ashton and A4 Bath Road sites, for more information see The Bristol City Council website (http://www.bristol.gov.uk...)