Head to the Cooper Dean Roundabout near Bournemouth Hospital. On the opposite side of the Wessex Way to the Toby Carvery there's a bus stop on the slip road where cars join the dual carriageway. It's an ideal spot to wait for a lift to Salisbury, and if you can get to the A36 on the west side of Salisbury you should be able to find a lift to Bristol.
North towards Southampton, London (M3)
From From Poole or Bournemouth, take the bus M2 until the stop at the corner of Ashley Road - North Road, from there walk in direction of Sea View and walk Sea View road and further north on Ringwood Road. After about 1-2 miles you will be at the corner of Herbert Avenue and Ringwood Road and you can hitch just before the bus stop facing the Shop-Post Office. If you go up Ringwood Road just about a mile further, there's two more roundabouts - if hitch after the last one (where there is a bus stop) you're on the main Ringwood road where all the traffic passes you by. The best option is to accept a ride at least until Southampton Services although there might be some potential spot along the road to Ringwood before the motorway starts.