It seems literally unbelievable that anyone is contemplating a bridge over taxiway alpha.
Such a bridge would need to offer clearance over the taxiway of at least 50ft (a 737-800 is over 41 ft high), to say nothing of having a single span wide enough to accommodate wingspan and tolerances.
This is in addition to the climb from the level of the Parkway station. What's more, vehicles/trains/buses using the bridge would have to either descend to a "station", or a high-level station would have to be built in the CTA.
I struggle to understand how a tunnel would be affordable, but it would at least bring passengers to a point from where they could easily access the terminal whereas a bridge would, in my mind, present too many engineering challenges.