BATMAN
This time, I'll show you an example of how I do my adaptations!
Research:
Note- Batman is a character who has existed for over 75 years and has changed a lot over various media. So, rather than adapt any particular version, I decided to list those traits most often affiliated with him, and which made most sense *to me*.
Background: Bruce Wayne saw his parents shot dead in an apparent robbery as a child. This caused him to grow up determined to help fight crime in Gotham City. He did this by studying criminology. However this led him to realize the numerous legal loopholes used by organized crime to avoid prosecution- not to mention how deep corruption ran in the city. Furthermore, he discovered his parent’s deaths weren’t accidental- it had been a ‘hit’ ordered by a Mob Boss whom his father had “offended” by refusing to work for him.
Wayne was now obsessed with bringing an end to organized crime in the city, but also realized there was only one way to do so: by learning their secrets and exposing them to the authorities. To this end, he appropriated a prototype stealth suit that Wayne Enterprises had been developing so he could enter the lairs of mobsters or their agents and obtain evidence that he could then present to his contacts in the police (not for use in a court of law, as illegally obtained evidence is not admissible, but to provide them with intel that would help honest cops in their own crime-fighting operations.)
As a side effect of his efforts however, an urban legend of a “Bat-Man” sprung in the city, since his suit projects a bat-like silhouette in the dark. Most people don’t believe in it and Wayne himself doesn’t care, although those who have come to meet him call him “Batman” for lack of a better name.
Powers: Batman is well-known for being a major hero without powers. However in BASH some of his skills and Equipment count as such. We’ll cover them in the appropriate sections.
Weaknesses: Again, none.
Equipment: I’m going with the Stealth Suit option from “Batman Begins” to explain his silly costume. This would be a Power (Transparency 2 /Translucent, Only in Shadows\ 2 points) with no Gadget limitations (it cannot be stolen while he’s conscious.) The “ears” are radio antenna for his bugs (see below). And the cape is for Gliding (/Gadget, Fragile\ 1 point) again to justify his carrying around such a cumbersome thing. Maybe it’s in case he falls from a building.
As for the bat-belt, I know many people like giving him either Conjuring or Gadgeteering for this, but most evidence I’ve seen shows him using devices made by his company rather than by him, and there was even an official list of the belt’s contains once. Therefore I decided to use Equipment instead. He has pretty much every item in the list, except Hi-Tech ones like blasters; but the only pieces he consistently carries are batarangs (boomerangs), bugs (1 CP), and a grappling hook and rope (for climbing.) He probably also carries tools for gathering evidence: a lockpick gun, a camera and a hacking drive.
Let’s also give him the Power Weapon Technique (Boomerangs) (1 pt) so he can use his weapons to the fullest.
Advantages & Disadvantages:
I choose the following Advantages for Wayne:
Appeal (I lost count of all the women, good and evil, who have had crushes on him)
Contacts (primary: Commissioner Gordon, Harvey Bullock, Renee Montoya)
Frightening Presence (more from his attitude than his looks)
Furtive Movements (if you’d rather not use the stealth power, use this)
Headquarters (The Batcave)
Membership (Justice League, Outsiders, Batman Family, or whichever)
Resources
Sidekick/Pet (usually (a) Robin, but sometimes Alfred or even Ace the Bathound)
Super Vehicle (The Batmobile, which should be more of a stealth than combat vehicle. He has had others as well, but this is the best known).
As for Disadvantages, I pick:
Arch-Enemy (No, not the Joker, but rather, Ra’s al Ghul, who is both a match for him and a natural enemy for being the head of the League of Assassins)
Normal
Rogue’s Gallery (Gotham City Criminals; most Batman Villains are no match for him either physically or intellectually, and they’re not his main target anyway).
That’s six Advantages more than Disadvantages, so we have to account for them some way. I assign six Setbacks to Batman now.
Additionally, Batman has been described as having trained to peak physical and mental condition, so we give him a Score of 2 in all Stats.
Mental Malfunction: This one is well-known: “Sworn to Fight a War on Crime”.
Skills:
Batman is known as “The World’s Greatest Detective" and has been known as “The World’s Greatest Escape Artist" (not that necessary, but let’s keep it) so he gets Investigation/Finding Clues and Escapology/Improvising, and spends his skill slots for a +2 bonus each. He’s also “one of the World’s greatest Martial Artists" another thing I find unnecessary but If you want, give him the Power Martial Arts level 3.
Stats: As mentioned, he’s got Brawn 2, Agility 2 and Mind 2 (12 points total)
Hits: 100, as for any true Hero.
Breakdown: Powers 7 points, Equipment 1 point, Stats 12 points = 20 points
Setbacks: 6
Summary:

Batman (Bruce Wayne)
(Hero, Hits 100)
Brawn 2
Agility 2
Mind 2
Powers:
Gliding /Gadget, Fragile\ (cape)
Martial Arts 3
Transparency /Translucent, Only in Shadows\
Weapon Technique (boomerang)
Mental Malfunction: Sworn to Fight a War on Crime
Advantages
Appeal
Contacts (primary: Commissioner Gordon, Harvey Bullock, Renee Montoya)
Frightening Presence
Furtive Movements
Headquarters (The Batcave)
Membership (in a super team)
Resources
Sidekick/Pet
Super Vehicle (The Batmobile)
Disadvantages
Arch-Enemy (Ra’s al Ghul)
Normal
Rogue’s Gallery (Gotham City Criminals)
Skills:
Escapology/Improvising x2
Investigation/Finding Clues x2
Equipment: boomerangs, bugs, rope, grappling hook, lockpick gun, body camera, hacking drive.
Breakdown: 20 CPs, 6 Setbacks
And there you have it! Of course, I don’t expect everyone to agree with my take, but you can at least use it as a starting point; just change anything you feel is necessary. Remember than in a higher level campaign (read: when working with Justice League-level heroes) Batman gets Hero Points to compensate.