In all cases, readied actions, some immediate actions and attacks of opportunity, game flow is interrupted; an action is started, and that action itself, provokes a response. The response is then resolved, then provided circumstances have not changed, the action that was interrupted continues.
Although an interrupting action is resolved before the action that triggered or provoked it, the response does not retroactively prevent the action from starting.
attack of opportunity
An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
Then, any time before your next action, you may take the readied action in response to that condition. The action occurs just before the action that triggers it.
Some special abilities or spells use immediate actions in response to other actions (or consequences of other actions, like damage)
an immediate action can be performed at any time — even if it's not your turn.
In most cases, actions may not be split up, so an interrupted action that cannot be continued is no longer available (lost, consumed, wasted, whatever you want to call it). With Tumbling, it is during a move action that the check may be failed, so provided circumstances no longer prevent it, the move action may continue.
Even though an interrupting action is resolved before the action that elicited it, that eliciting action had to start in order to elicit the response.
Tumbling is not unlike moving out of a threatened square; it is the movement that provokes and it is resolved before leaving the threatened square, even though that action is what caused the provocation.
The Tumbling description does not mention whether or not you have to move back into your square.
Faliure means you stop... and provoke
On the other hand, Overrun does.
If you fail [...] you have to move 5 feet back the way you came, ending your movement there.
As does Bull Rush
If you fail [..], you move 5 feet straight back [..]
If you treat Tumble like Overrun or Bull Rush, then there is a movement cost for entering the square, then failing and going back.
If you treat Tumble like it's written, then you would ignore any movement from the failed attempt.
I think it would be unfair to impose penalties not listed (like interpreting stop as ending your movement), but I do think using the movement cost in Overrun as a guide for tumble makes sense, as both are attempting to move through an enemy's square (as noted in the descriptions under Movement Position and Distance -> Moving through a Square).
If you treat Tumble as written, and different from Bull Rush or Overrun, then in your example, Abe moves 10' then attempts to move into Bob's square, but fails. There is no cost to the attempt, so Abe has 20' of movement left.
As Overrun and Bull Rush
However, if we treat Tumble like Overrun (and Bull Rush); Abe uses 2 squares (10') of movement to approach Bob, two more squares (10') to attempt to move into Bob's square (since it's difficult terrain), where he fails his Tumble and uses two more squares (10') moving back out. If he can otherwise continue (Bob's attack of opportunity didn't change circumstances), Abe would be able to move, although at this point, he's used 30' of a 30' move action.