No union shop is going to hire street Captains. What is happening at places like Mesa is that Captain bids are going so junior, that people still in new hire training are getting the awards. Companies usually cannot or will not predict (at least not officially) whether this is going to happen to anyone in a particular class, all they can say is what has happened in previous classes / bids.
If they sense it is going to happen, or it has been happening and they have reason to believe it will continue, then they will route the higher time new hires into the aircraft type in question. Exactly what criteria they use is unknown but common sense would dictate that people who meet the minimums for Captain who have prior 121 time, prior company time (furloughed major pilots coming back to their "roots") would probably be the best suited candidates for the job, along with those who already typed / have experience in that aircraft type.
In reality it's almost impossible to really predict what criteria they're going to use because they themselves don't know exactly. They know what they like and need, but they're not going to know what plate of candidates they're going to get until it happens.
In the end, they will assign you an aircraft that they need you in. You can bid for whatever you want, but you cannot specifcally apply for a Capt. position.
As for non-union airlines, I don't know. Since they are not bound by a union contract, they can put whoever they want in the left seat, provided they meet insurance minimums and pass training and checkrides. In your example of a guy with boatloads of 135 time, then yeah, sure he could get on with them. However, if he's up against 25 guys who are typed / current in the aircraft they're hiring captains for and have been flying those aircraft under 121 for someone else, then I'd say your 135 Turbine Wonderboy isn't going to fair so well. BUT, having said all that, if the 135 Turbine Wonderboy knows the Chief Pilot real well or has some other solid connection with the company, then he's probably got a good a chance as any of the 25 121 Perfect Matches.
Hope this helps a little.
Ray