I’ve driven it twice in the last 2 years, most recently at the start of May this year.
It’s a good 11-12hrs solid driving from Calais, and i think the easiest routes are either heading up the French coast into Belgium, then south past Brussels, into Germany and straight down past Stutgart, Ulm etc into Austria, over the Brenner Pass, through Into Italy and all the way down to Verona before cutting in towards the south of the lake. Very few tolls on this route (only a few euros in Italy plus the tax in Austria.
The quickest route was Calais, Reimes, Metz, then snake down through Luxembourg heading for Milan then over to Garda. Tolls here through France and bits of Luxembourg plus tax in Switzerland (about 40 Euros)
The most scenic route was Milan, Chamonix and up through France, but this was the most costly due to Mt Blanc tunnel.
There’s barely an hours difference between any of the above tbh.
We had another fantastic weeks riding in the mountains at the northern end of the lake. Plenty of places to hire bikes if your not taking your own, and loads of shuttle companies.