It wouldn't take much less than 2 hours to get from central Liverpool to Windermere by coach, so the train link I suggested doesn't "cost " time that you wouldn't have to spend any way. You'll see scenery from train or coach.
You might find adverts for one-off day trips (as Grahamopolle says, mainly aimed at old people) in local newspapers etc - not so much online, as, perhaps wrongly, coach companies assume old people don't use internet.
May isn't high season - there are probably more tours in July / Aug, and weekends throughout year - so for 15th May, you'll have to think a bit more laterally, which was the basis of my suggestion to get train to Lakes, then a tour from a Lake District town.