Yes, Stokell, the lift bridge opened a week early, I've been riding over it since yesterday.
You might want to try The Plains Rd./ York Boulevard entrance to Hamilton through Burlington instead of the beach. It's a much nicer ride - You pass the Royal Botanical Gardens, Dundurn Castle, Cootes Paradise, downtown Hamilton (not the highlight of the trip) The rail trail up the escarpment is accessible from Wentworth Street.
If you are insistent on travelling via the beach, there is a nice wide new asphalt bike trail along the lakefront from Joseph Brant hospital in Burlington, extending past Confederation Park in Stoney Creek.
The rail trail does go to Caledonia, there is a gap around the Lincoln Alexander Expressway in Hamilton, but it's not too difficult to find your way back to the trail. I can give you directions if you need them. This trail is a little rough for a road bike, it's paved but just tar and chip.
Sorry, I don't have any info on the York portion of the rail trail.
For off road trails, the Dundas Valley is great check
freewheel cycle for maps. Red Hill Valley in East Hamilton also has some good bike trails, with linkages to the Bruce Trail along the escarpment. Check the City of Hamilton website
here and click on "Parks and green spaces" for a city map including bike trails.