I worked for a temp agency and they put me in a bail bonds office, a person in jail needs someone to “go bail” for them. Well that’s the term we used.
From what I saw, if the bond is set under a thousand and the offense is non-violent and the person doesn’t have a record, they would most likely just keep saying to the person, try to find someone to come in a put up the bond. If you had no one, the would issue an “I-Bond” which in Illinois means they let you go on your word.
I’m sure different states call it different things.
I would think the cops wouldn’t escort you to an ATM as it would be a nightmare if something happened and the person came back with, the cop was trying to exort money out of me. It’d be easier to I-Bond you.
Some places even take credit cards, so you could even get yourself out that way. It’s possible to earn points for bailing yourself out. 
The thing to remember is cops don’t want you in jail. Judges don’t want you in jail and the prison officers don’t want you there. It’s too crowded already.
So unless you’re a real danger to society, they’ll be pretty co-operative about keeping you out.
When you’re in custody, the police or prison is responsible for you. After seeing the type of people in jail, I wouldn’t let anyone I HATE stay in jail rather than bail them out, if at all possible.
When I first started there, we’d have people not show up, so I would call and say “You missed your court date, you need to come into the office so we can, get you rebonded out.”
And they’d come in, go to the station, and in a few hours be bonded out at a higher bond, another court date. And the same person could keep doing this. I remember asking the owner why judges allowed this, as the person is making no attempt to show up.
The owner said, “Judges don’t want you in jail, if you don’t have to be. If this person is missing his court date but turning himeself in, he’s not likely to flee, so the judge just reschedules” The owner didn’t care as he made more money. I had one guy do this FOUR times before the fifth time he showed up. He wasn’t violent, he’d just go out and get drunk and be a public nuisance.
I should say what I said applied to Chicago and Cook County Illinois, and it’s the second biggest county in the USA (population), so a small town county might be somewhat different.