Inside Job is played.
You encounter the first piece of Rezzed ICE (let's call it a Tollboth).
You have two effects in play:
1) Runner: Bypass the first piece of ICE encountered
2) Corp: Make the Runner Pay 3 Credits
The Runner is the active player, and chooses the order of their pending effects first, in this case, to bypass the ICE.
As the Runner is no longer encountering the ICE, the Corp cannot enact the Toolbooth effect.
This is the correct timing/order. It is important to remember that this is not MTG there is no stack. Therefore the runner gets to choose which things that "would" trigger, to address first. Choosing Fem first means that by paying X-credits the runner bypasses the currently encountered ICE. The game then looks at the run and determines no ICE is currently being encountered and the strcuture of a run dictates that the run can/must approach the next ICE. This also means that Fem avoids things like chum etc. because again the "when encountered" part of chums routine never gets a chance to trigger before it is bypasses. Though of course the runner could choose to trigger things before fem, but that would be a really bad idea.
I'm not sure what you mean but just to be clear if you use Femme to bypass the next ice after encountering chum (and letting chum's routine activate) you will actually take damage from chum even though you bypassed the next ice since you never broke any subroutines.
Edited by frybender