That gap (pun intended) by the Glenwood Bridge/Homestead/Sandcastle (I think this is what you're referring to) has been the last missing piece of the puzzle for a while now. It is under construction to supposedly be fixed by November 11, 2011 (11/11/11) and we shall see how it goes with that deadline.
Sandcastle, an amusement park, owns that parking lot and people have had varying experiences with them. If the place is open, people have sometimes been able to ride through their parking lot access road. Then, from right under the bridge to the west, alongside the railroad tracks it is possible to walk and push a bike for a hundred yards or so until it connects up with the South Side Trail (Three Rivers Heritage Trail is the name for the whole system, including trails on both sides of all three rivers, though it appears as such on Google.). There has also been a construction project for a water system, somewhat near where Becks Run Road dead-ends onto East Carson Street, which has cut off trail access, though that project may now be concluded.
The 28X used to be run with mini-shuttle buses, which I don't think had racks, but has lately been serviced with full-sized buses which should have the racks. Another option to consider would be to leave your bike and baggage in town, ride the bus, pick up the car, and come back to get the rest of your stuff. Depending how much you're loaded down, it may just be easier if you are in a less unwieldy state. Also, your rental company may have a bike rack on the car or something, but if you're planning on taking a wheel off and putting it inside, they might give you a hard time about possibly messing their upholstery.