Watch: Batman Vs. Superman Fighting Styles
It's been said that Batman is a master of well over a dozen forms of martial arts (or any given number), which would include jujitsu, karate, kung-fu, their derivatives, inspired fighting styles, etc.
A video below takes a look at the techniques used in Batman Vs. Superman and attempts to figure out what forms of martial arts Batman uses in his techniques.
My two cents regarding what martial arts Batman would use would be a style that incorporates everything, and I'm guessing Batman would put it together to form his own style. I'm actually a martial artist myself, and the style I train in does just that with Danzan-Ryu Jujitsu (here's a link to our top Sensei). While many people are familiar with BJJ, Judo and cage fighting, those styles, IMO, aren't as effective in the real world or street fighting due to rules (they are sports). True martial arts is about war, and there is no rules in war. So my guess is Batman would train in a form of small circle combat jujitsu with no rules. It would be almost like comparing the stuff done in The Matrix (more Kung Fu/Hollywood) to John Wick.