The Algonquin Parkbus runs until at least October 13th - after that it switches to an as-yet-unannounced winter schedule. However it stops going to and from Algonquin the last weekend of September. On the matter of hiking, they say:
Highland Backpacking Trail (19 & 35 km loops) is easily accessible via our Lake of Two Rivers stop. Short 800m trail leads to Mew Lake office, where backcountry permits can be picked up. The Western Uplands Backpacking Trail (32, 56 and 88 km loops) can be accessed via West Gate stop, where permits are available (trailhead is 2km down the road)
If you're not familiar with your options around hiking in Algonquin, check the Friends site. You can certainly go for two days if not longer.
In October the bus goes to Killarney, which also has lovely hiking trails:
Killarney Provincial Park offer some great day hikes that are easily accessible directly from the George Lake Campgrounds. The campground also serves as the trailhead to the famous multi-day La Cloche Silhouette Trail (78km loop, 7-10 days), only recommended for experienced backpackers.
Grundy Lake has only day trails and French River doesn't have hiking. So this solution will carry you through September (but plan carefully to make sure you can get back home on this bus since it doesn't run every day) but not into October.