Far from being a Bourne expert, but from what I've read, higher-tier characters from the Arrowverse (Ollie, Malcolm, Nyssa, Island!Slade and Billy...) should be able to win 1, maybe 2 (depending on the result for 2, maybe 3. Ollie and Malcolm have good shots at winning due to explosive arrows). Bourne with prep should win 4, barring Malcolm bringing the earthquake device with him, and surviving long enough for it to go off.
Also, I suggest Reese from Person of Interest for a good shootout match (casually kneecapping a running guy from a good distance is easyb for him). His defeating a SWAT team while basically dying suggests that 1 wouldn't be a complete stomp in Bourne's favour, either...