By the way you did ask for gardens on the west coast.
The Mountain Goat does run a very good tour to Muncaster Castle whose gardens should be looking great. However they miss out Eskdale watermill, Stanley Ghyll waterfall and The Japanese garden at Giggle Alley, Eskdale Green.
They also don't stop at the Roman Fort on the Hardknott Pass, and don't give an option to use La'al Ratty- the narrow gauge Ravenglass and Eskdale steam railway. They also miss out the wonderfully located Eskdale Church.
For someone coming through Eskdale I would recommend the Woodlands Tea Room at Santon Bridge.
Any bus tour has to make choices, no tour can include everything.
To do all of that you would need a private driver. I actually would suggest a driver one way, then train/bus (a very scenic stretch of rail line) the other.
From Muncaster Castle to Ravenglass it's a lovely walk through the woods and past the Roman Bath House.
For someone with a hire car that is a great one or two day trip out of the Central Lakes. On a two day road trip, depending on budget, I would suggest staying overnight at Irton Hall, although there are other options for a more frugal budget.
Adding in St Bees, Whitehaven etc it could easily be a 3 day road trip.
Another garden on the West Coast you won't find in a guidebook is Distington walled garden- accessible by bus every 15 minutes, but best by car.