Note: this is an "in theory" collection of information. Specific numbers and whatnot may not be of too much help unless you have all personal perks (education, possibly stats). This should however provide a good idea of what to expect and the concept of how to predict your outcomes.
Note 2: This is still work in progress, irrefutable feedback is much appreciated, "I believe there exists something like this hypothesis" not so much.
Note 3: Busting score was added to DoctorN.

~ Busting ~
Busting people out of jail is a big part of Torn, with merits drawing in any player to commit to it at some point. It is also one of the aspects that has changed a lot since I started playing, but let's not get nostalgic.
Busting has a couple rather simple mechanics, so I'm quite surprised there is no script to calculate success prediction. These are the four known mechanics that come into play:
1. Level.
2. Minutes in jail (possibly seconds).
3. Bust cooldown (busts within a specific time).
4. WTF (= variable factor adjusted at any time by staff without notice).

~ Busting Perks ~
Faction: Criminality - Jail time: Decreases jail times up to 30%. (2% per upgrade).
Faction: Bust skill - Increase bust skill up to 50%. (5% per upgrade).
Faction: Bust nerve - Decrease nerve bust cost up to 3. (1 per upgrade).
Law Firm: 5* - Easier to bust more people at once.
Law Firm: 10* - View success chance of potential busts.
Education: Gain a 5% bonus to your skill in busting.
Education: Gain a 10% bonus to your skill in busting.
Education: Reduce the chance of being caught when trying to escape from jail.
Education: Use less nerve when trying to escape from jail. (unknown factor).
Education: Gain two bonuses - Busting is 50% easier and buying is 50% cheaper.

~ Books ~
Shawshank Sure Ain't For Me! - Large jail bust & escape boost for the next 31 days. (Allows you to bust 2-4x as many people per day)
A Job For Your Hands - Increases dexterity by 5% up to 10m upon completion. (If dexterity effects bust)
Fight Like An ******* - Provides a passive 25% bonus to all stats for 31 days. (If dexterity effects bust)
Weaseling Out Of Trouble - Provides a passive 100% bonus to Dexterity for 31 days. (If dexterity effects bust)
No More Soap On A Rope - Decreases all jail times by 50% for 31 days. (Mainly helps others bust you)
Memories And Mammaries - Takes the same effect from the last used book for 31 days. (Highly recommend using this with gym books)

~ Unconfirmed factors ~
Dexterity: Confirmed to not be a factor by staff.
Level balance: your level in comparison to the target bust, likely an outdated factor.
Number of busts: The more you bust the easier it gets, likely a cap of 1000 busts if still active, although you could get minor benefits further down the line.

~ Busting Cooldown ~
The busting cooldown most likely have a linear timeline, with an expected soft-cap at around 6,000 score and hard cap at around 10,000 score. Let me explain it this way:
Lvl 30 * 134 min = 4,020
Lvl 20 * 145 min = 2,900
Lvl 23 * 183 min = 4,209

If you wanted to bust those in succession, you would reach an 11,129 busting score that would need to cool down for a period of time before you could bust another person. Busting a 4th person within the same busting spree would likely fail, or land you in jail.
*Unknown factor* Busting a 2,500 score target and then an 8,000 score target would likely fail, while the opposite is true if you reverse the order. You want to go from harder targets to easier targets instead of the other way around. Why this is true is unknown.

~ Merits ~
(M) Bust 250 people from the Torn City jail
(M) Bust 500 people from the Torn City jail
(M) Bust 1,000 people from the Torn City jail
Bust 1,000 players out of jail
(M) Bust 2,000 people from the Torn City jail
Bust 2,500 players out of jail
(M) Bust 4,000 people from the Torn City jail
(M) Bust 6,000 people from the Torn City jail
(M) Bust 8,000 people from the Torn City jail
Bust 10,000 players out of jail

~ Bailing ~
Bailing is a lot easier than busting, mechanically. It’s simply level*minutes. It’s simple as that, although you can bring down the price quite a bit by using the mechanics given to you by the game.

~ Bail Perks ~
Law Firm: 1* - 50% decreased bail costs.
Education: Gain the ability to buy yourself and others out of jail while you are in jail yourself.
Education: Gain a 5% discount when buying people out of jail.
Education: Gain a 10% discount when buying people out of jail.
Education: Gain two bonuses - Busting is 50% easier and buying is 50% cheaper.

As someone who has all perks in buy out price reduction, my calculation would be this:

Time	Level	Time*Level	Price $	Price per level
226	22	4,972	213,494	42.94
353	60	21,180	908,010	42.89
353	56	19,768	847,476	42.87
353	58	20,474	877,746	42.87
353	54	19,062	817,209	42.87
383	52	19,916	853,632	42.86
404	36	14,544	623,295	42.85

With that data I can reason that the actual buy out price is $43 per minute, deducting the seconds passed making it .85-.94 making this list an equal bust out difficulty:

Time	Level	Time*Level	Price $	Price per level
100	10	1000	43,000	43
20	50	1000	43,000	43
10	100	1000	43,000	43

This basically dictates that a level 100 with less than 10 minutes in jail is easier to bust than a level 10 with over 100 minutes in jail. Another thing to notice from the first table is that the longer someone is in jail, the lower the price per level - so there could be some sort of discount the longer someone is in jail instead of my theory.

Bust cooldown is based on the buy out price (bust difficuly) as well as how many busts you have made within recent time, 8hrs seems to be the complete cooldown time to remove all busting cooldown (assuming you reached a 10,000 bust score).
From my experience you can bust out 3 people from jail in succession (within minutes) 3 times a day. This is assuming you keep their bust out difficulty of below a factor of 3,600 (time*level) or $154,800 assuming you have all perks related to busting.

~ Awards ~
Bail 500 players out of jail.