Wimps!!
Cycling is fine if you miss out the dual carriageway -... go all the way through Boscombe, past Pokesdown station, down the hill, keep following the road down and you will travel along an A class, mainly residential road until you get to the bridge that crosses the Dual carriageway.
Straight over the lights, left at the mini roundabout 3/4 a mile up the road and Bobs yer Uncle, Fannys' yer aunt. (Check the route on a map tho - it's almost, but not quite, as straightforward as that)
There are showers in the changing rooms. Its a 15 - 20 minute ride from the centre of Boscombe, unless you own a bike akin to Mary Poppins.