A bondsman was in the vehicle. Cindy was taking her back to jail following the issue of KC warrant. She got a call that there were protestors waiting at the jail, and did not want to be in the middle of that mess.
The bondsman is allowed to enter the "Sally Plaza" entrance, but no private civilians, so no protestors, but CA is not allowed there either.
They switched cars under the bridge to avoid cameras. As is common practice, they BB was in an unkown SUV to LE (Padilla and company frequently used this practice to evade media) so KC surveillance detail stopped them because to them it could have been an attempt to flee for all they knew, and took her in..
Baez was in neither vehicle, that is correct.
ETA: sorry, meant to say this account is from LP, as told to him by one of the agents in the car that took her in.