I would say your best bet is to take the 51 bus up Main St. West (becomes Wilson St.) to the end of line (see
link), and then continue up the hill, where the Bruce trail crosses Wilson St. heading west (it will be on the right side of the road). This is my favourite part of the Bruce trail in the area, and you can check out Tiffany and Sherman Falls which are just off the left side of road (two waterfalls everyone should see at some point).
It's hard to miss the Bruce trail in Hamilton. Basically every trail in the area is part of it or a sidetrail to it.
Let me know if you need any other help, I've spent a lot of time on the trails.