It's a gorgeous walk!

Cross road into Hyde park... you then have two options... more pleasant is to walk along the 'Serpentine road' passing the Serpentine lake, then turn right at the car park until you hit Lancaster gate, you're then just a couple of mins from Paddington. Overal its probably a 20-30 mins walk

Quicker is to turn right up the path when you get into the park.... up to Speakers corner, then left along Bayswater road... or up Edgeware road for a Turkish breakfast pastry and coffee.

Both these routes should be pretty clear on google maps

Bus at that timeof the morning however will be quicker.