Sly first found Bentley in the orphanage they both grew up in and they soon became best of friends. Then, with their pal Murray, they formed a band of thieves and started small thefts. Bentley, being the smart turtle that he is, became the brains of the group and typically made all the plans for their heists and hacked into any computers when necessary.
During the ending of Sly 2, Bentley was helping Sly defeat Constable Neyla, that had the newly re-established Clockwerk pieces, when he accidentally came too close to the mouth of the massive bird. This incident injured his legs to the point where he became permanently handicapped from the waste down, which caused him to be stuck in a wheelchair for the remainder of his life.
In Sly 3, Bentley found his first real love interest with the Remote-Control expert Penelope. He of course, thought that no one could be interested in someone in a wheelchair and tried to avoid her most of the time. Then, when Penelope was kidnapped by Captain LeFwee, Bentley finally decided to take action. He ended up saving Penelope and that started the relationship between the two.
After the adventures of Sly 3, Bentley was seen living a happy life with his new girlfriend. He was also trying to come up with a way to create a time machine (most likely to un-hypnotize Sly who started working for Carmelita Fox near the end of the game).
In the first game, Bentley was merely the one who gave Sly information on how to perform certain tasks, you did not get to play as Bentley in the first game.
Band of Thieves
The second game however, allowed you to finally play as him. Bentley's main abilities included: using a crossbow, throwing grenades, and hacking into terminals.
The crossbow worked as a tranquilizer for the game, you aimed the cross-hair at the the enemy, press the R1 button, and soon the enemy would be disabled for a set amount of time.
The grenades could either be thrown at, or set on an enemy. If you chose to throw the grenade, you had to choose the power of the throw, and what direction you were throwing the grenade in. Setting the grenade on the enemy worked by sneaking up behind the enemy, pulling out a grenade, and then placing the grenade on a part of the enemy.
Hacking terminals was more of a minigame for the player. You start out as a small colored tank-like object. You use the left analog to move, and the right analog to shoot. Your main objective is to make it to the access point on the other side of the level. While on your way, you'd encounter switches to turn on and enemies to shoot. Reaching the access point, allows Bentley to hack into the terminal and then Bentley can use the computer later in the game for the final heist.
Honor Among Thieves
Although almost exactly like the gameplay of Band of Thieves, this game brings a slight adjustment to Bentley's style of gameplay. Since Bentley is now in a wheelchair, he cannot travel as fast anymore, and he also uses more automated stuff for throwing grenades and shooting tranquilizing darts.
Thieves In Time
Bentley returns in the 4th installment being confirmed to still be in a wheelchair with more gadgets.