Stagecoach Lake is south of Steamboat Spgs and is a jet ski haven.
Steamboat Lake is north of town near the community of Hahns Peak.
Different places.
Whatever your plans - get a plastic laminate map of Routt National Forest.
It will be an invaluable resource. You can view it online here:
Routt National Forest - Paper Maps Online
But remember, electronic access will be limited. Very limited.
Have you considered a loop via Steamboat Lake - mostly paved the first day -
Then Hogs Park just across the border - continuing on to Walden in North Park -
Then back across the Park Range to Steamboat via Buffalo Pass?
None of those roads is that difficult on a mountain bike -
Perhaps a few steep sections - sometimes sandy or rocky - varies year to year.
Downhill can be trickier than up - just keep your speed under control.
You can random camp on national forest or BLM anywhere for free.
Maybe having the park the first night will be reassuring -
But campsites will really be no problem.
Bring a plastic trowel - hang your food.
(Raccoons are probably more of a problem than bears.)