There are 8 in Bournemouth. Try this link:http://www.nearestbeach.co.uk/dog-friendly/bournemouth/
Personally I used to like Lake Rd in Poole. If the weather turned out to be windy, we walked around the lake instead. This is not the smartest beach in town though.
Thanks everyone. I'm now home and had a great 3days. Dog had a fantastic time at Bournemouth, Poole and Lulworth as well as a couple of country parks nearby