Well, taking the obvious
Lyers never lie -> False -> Bill is a Lyer;
Bill is from the same district as me -> True -> Bob is a Lyer who spoke truth, contradiction
Bill is from the same district as me -> False -> Bob is a Truthamer who lied, contadiction
Bob speaks Paradox
This implies that something else is required.
Easiest is that Bob is from a second town, named Paradise
Lyers never lie, they sleep sitting, they never fall down drunk, it's really quite marvelous. They do tell lies, but that's not necessarily what the question is asking.
This (fanciful) interpretation leads us to the following
Lyers never lie -> True -> Bill is a Truthamer
Bill is from the same district as me -> True or False -> Bob can be from either Trutham or Ly without contradiction
And now to determine Bob's district
We think to the bridge, if they were both from Trutham, or both from Ly, this seems an odd spot to converse on the job; a donut shop would be far superior. Clearly the Bridge is the point where their districts, and thus duties, overlap; and so Bob is from Ly.