You can start out intuitively. Suppose you are a bug living on a very large soap-film surface, and you want to set it shaking so that a soap bubble will break off with you inside. That is a lower-dimensional version of what you might want to do - create a hyperspherical bubble of brane-space that breaks off from your home-brane and travels into the bulk. The basic way to change the local curvature of a brane is to gather mass in the one place. What you want is to have a sort of three-dimensional "black shell" (like a black hole, but with a spatially extended singularity shaped like the surface of a sphere, rather than being just a point) form, with you inside it.
So let's suppose you had some way of forming a black hole of a certain radius (by shepherding enough mass into the same volume of space, until gravitational collapse took over). You could try to do that simultaneously at a multitude of points surrounding you, with the points close enough that the event horizons of the new black holes overlapped. The black shell would be made up of a large number of black holes that formed simultaneously. It seems that for this to work out, you would have to have lots of matter streaming towards you from every direction simultaneously - and then you time it all very precisely so that the black shell forms while it's all still a finite distance away, rather than part of it falling all the way into where you are located and destroying you.
This would definitely require engineering on a cosmic scale, e.g. stars being steered around (see "Shkadov thruster"), and flows of interstellar nebulae being planned in advance. It sounds like something that would require thousands of light-years and millions of years at the very least. Then even if you managed to break off a bit of brane, you'd have to worry about internal gravitational shockwaves from its creation destroying you. And then suppose you do meet another braneworld after an unknown time passing through the bulk, if it doesn't know you're coming, I see no guarantee that collision will be friendly.
What I just sketched is probably the crudest and most naive way of thinking about how this would work. Maybe there are gentler ways to break off a branelet in a controlled fashion, or maybe the whole thing can be ruled out by "energy condition" theorems (of the sort which pose problems for the existence of wormholes). But there's certainly no reason to think that FTL is possible in the bulk. Bulk space is just ordinary space.
Also, another thing to bear in mind is that braneworld models are not limited to 3D branes. You can have several branes of higher dimension which intersect in a 3D region, and then have strings connecting the branes which are confined to that region, and you'll have an effectively 3D space. In that case travel between braneworlds might involve staying on one of the branes but somehow getting away from the intersection zone.
