Biking to Conestee (swamp rabbit)

I was looking at Google maps and it looks like I can take my bike all the way down swamp rabbit to get to conestee, but I think I know the place whwre swamp rabbit connects into conestee ( the trail that goes over the bridge into the park) but isn't that a no bike trail? Or does the swamp rabbit trail connect somewhere bike accessible? Please note i will also habe a trailer to pull my daughter.