what's the process that had him in jail for so long, and is that a process that I could exempt myself from with money for bail, access to credit, lack of priors, money for a lawyer I already know?

The surprising/scary part here is the man jailed was driving an Alfa Romeo, so presumably he had some money for bail/lawyers, and was still jailed for a month despite no evidence.

Usually it's waving your right to a speedy trial. Very common in a lot of cases but the reasons are usually dependent on the circumstances