You don’t have to plan from scratch. These rides pass close to Mirror Lake, mapped and written up by route publishers around BC. The full maps and turn-by-turns live on their sites.
Loop Kaslo Slocan— Trails BC · 221 km route, passing within a kilometre
BT700 Kaslo— BT 700 Bikepacking · 85 km ride, passing about 1 km away
Getting there with a bike: province-wide buses, ferries, and shuttles are listed under Transport (some serving Mirror Lake may be listed there rather than here).