Can I go to Bournemouth Dog show as a spectator, is there an entrance fee and can I take my 7 month old puppy

Yes, not sure, and probably no. 

Looking at the schedule for it it says legally docked dogs can enter so there shouldn't be an entry fee for the public to enter the show however there is a £6 car park fee on the day. You can take your dog as a spectator dog for £5 on the day but There is no unentered dogs tent so if the weather if too hot or wet it will have to walk around the show with you.
You can get the schedule here
http://www.highampress.co.uk/download.asp

Thank you for the information, I only live a few miles away and my favourite are the west highland white and    The German shepherds so would be lovely to go and watch them.

But just consider the weather and how long you plan to stay before you decide to take the puppy - excellent socialisation for a short time, but a very long day if you stayed for many hours, plus the possibility of walking him/her round the showground in scorching heat or torrential rain. :-) Also it's quite likely GSDs and Westies could be on different days.

Terrier, working and pastoral are on the same day so yes westies and GSD's will be there

Ah thanks, hadn't looked to see if it was a 2 or 3 day show this year. :-)

Its been a bit confusing this year, some of the shows have had groups together that are never normally together.