I know it's not Bournemouth but I heard Jodie's fitness is really good. She's based in Poole near the indoor skatepark (prevail)
Mumology Movement - Sarah Scudamore
I second Sarah- she does buggyfit classes too! Or Laura Spinney does mum & baby classes in winton too
Mums the Word is really good, she has a few different classes - not sure how close she is to Wallisdown but it’s very baby friendly!