I found the wood when we were walking by the River Derwent in the Forge Valley Woods on our holiday in Yorkshire last November. Sloe wood is beautiful to turn.
I marked one centre on the end of the handle near the bark edge and at the bowl end near the centre of the log to give a kick to the handle and mounted it on the lathe.
I suppose you could spend time rounding the handle more but I find it OK to proceed gently with a spindle gouge. You can also turn the sides of the bowl to get a nice symmetry (but you're turning air a lot of the time!) and a decorative knop on the end of the handle.
Give it a burnish with a handful of shavings and carve out the bowl...