Sandra, no pics specifically of the walking route but the best compromise of proximity to Scafell and to fast public transport is the Langdale route, go south side of the valley from NT campsite, and then follow the ridge up to the west and then map it from there. Campsite in Wasdale, or an expensive hotel in Wasdale (with public bar for food), then come back via a slightly different route. If you want to make a loop of it then come head back northeast and then down into Borrowdale, then bus down to Keswick. Or, back north and into Buttermere? Scafell-Grasmere you can avoid dropping down into the valleys so less climbing but more distance. The campsites-peaks has more climbing, so when mapping the walk look at height climbed not just distance.
Grasmere to Scafell will need you already "fit" so it might be best done if you're young on the 3rd day of a loop. Grasmere has plenty of B&B, but NO camping, but e.g. if you've been camping in Langdale NT and camping in Wasdale, then a B&B after a long walk to Grasmere will be a luxury. From Grasmere a fast bus down to Windermere train.
Pic of the view of up the valley you'd be walking up the south (left) side as you climb out of Langdale. I've biked all around the roads close to Scafell.
above pic the campsite is effectively where the words "low gear now" is down in the valley hidden
this is pointing to the route you'd take heading to Scafell
I'll be in those places in a 4-day Lakes trip late September.
