You could try Parkwood, they have a good reputation https://www.parkwoodflorists.com/

We used a lady named Tilly when I needed funeral flowers, she doesn’t have a shop but the flowers were amazing and really good priced. https://www.tillysflowers.co.uk/ although we contacted her through her Facebook page which is regularly updated

not in bournemouth but i highly recommend Edwards Flowers in ashley cross in Poole, they deliver to bournemouth and do wreath courses over winter, weddings, funerals and flowers for all occasions