If you’re going into the park, you’re going to make quite a detour unless you only drop onto North Carriage drive (at bottom of Connaught gardens) and then come out again where the west carriage drive hits bayswater. Theres no legal route from the top of west carriage drive westbound inside the park.
I regularly ride in the area, and can recommend the bayswater road westbound is pretty safe, wide, and well surfaced all the way to the SB roundabout. Just watch some of the traffic at NHG where the roads narrow a little.
the route west from Euston via Harley Street/Marylebone/Portman is quite enjoyable, although its actually nicer riding eastbound (Wigmore, Cavenish, Mortimer)