APFT alternate event; bike. Can you bring your own bike?

You can, you just can't utilize the gear shifts.
The test administrator is supposed to inspect the bike to ensure that the gear shift is rendered inoperable via tape or mechanical disconnection.

First, I really appreciate this question as many do not realize that this has two courses of action; 1) I have attached two images that show the exact APFT 6.2-MILE STATIONARY CYCLE ERGOMETER TEST. 2) You can actually bring your own equipment as others have already mentioned. Although, I personally have own seen the stationary cycle ergometer test.

As the regulation, FM 7-22, Appendix, (dated 26 October 2012), specifies the following:

1) EQUIPMENT (APFT 6.2-MILE STATIONARY CYCLE ERGOMETER TEST)

The event supervisor requires two stopwatches (the timer and back-up timer each require a stopwatch), FM 7-22, Appendix A, and one stationary cycle ergometer. The ergometer must have mechanically adjustable resistance measured in kiloponds or newtons and must be available for training and testing. The seat and handlebars must be adjustable to accommodate Soldiers of different sizes. It should have an adjustable tension setting (resistance) and an odometer. The resistance is set by a tension strap on a weighted pendulum connected to the flywheel. The cycle ergometer must be calibrated prior to test administration. Event scorers require a clipboard and black pen.

2) EQUIPMENT (6.2-MILE BICYCLE TEST)

The event supervisor requires two stopwatches (the timer and back-up timer each require a watch) and FM 7-22, Appendix A. One-speed or multispeed bicycles are authorized for use. If a multispeed bike is used, the event supervisor and/or scorer will take measures to ensure that only one speed is used during the event. This can be accomplished by taping the gear shifters. The Soldier taking the event sets the speed by selecting the gear they wish to ride in. Event scorers require a clipboard, numbers, and black pen.

I always thought it was a BYOB type of a event.