Beyond the map there is only forest. No bike can go there, and it is part of the appeal of the region that the surrounding tarmac skirts it.
The nearest rideable road runs along the Stevens Pass Highway, US 2, which crosses the Cascades from Everett to Leavenworth at about 1,240 metres. It is a decent ride, with smooth surfaces, big tree-lined curves, and a sequence of river valleys, the Skykomish on the west and the Wenatchee on the east. The little Bavarian-themed town of Leavenworth, on the dry side of the pass, is the best-known stop, and Lake Wenatchee is a pleasant place to swim on a hot day.
For swimming, the lakes on the east side are your best bet. Lake Wenatchee is warm by mountain standards, with sandy beaches and views of the peaks. The rivers are cold and fast, so be careful of the current and the snowmelt. Glacier Peak itself, the volcano that sits at the heart of the wilderness, last erupted a few centuries ago, and from the highway it never shows its full face. What you get instead are snow-streaked ridges at the end of a side valley, cold air pouring down from the high basins, and the cedar-and-resin smell that follows the rivers all the way down to the lowlands. Mountain goats and black bears live in that country, and the occasional hiker emerges at a trailhead with the glazed look of someone who has not seen a road for a week.
Services are limited on the pass. There is fuel in Skykomish and at the little towns on either side, but you should fill the tank in Monroe or Leavenworth before you start, and carry a layer for the summit, where it can be many degrees cooler than the valleys. Winter closes the pass sometimes for avalanche control, and tyres or chains may be required. In spring, the snow melts and the rivers run high, and the waterfalls along the road are at their best.