A silicone adhesive may work, such as RTV silicone sealant. One important factor is the degree of cure of the silicone rubber to begin with. Fully cured silicone is difficult to bond, but freshly made parts are often not fully cured because of the time it takes. These can be bonded without special treatments.
Well, the Silicone structure that I'm trying to bond the TPE to is already fully cured into a mold. Let me also add that the silicone structure is much like a balloon, which is why I need the bond to be flexible, because when filled with air, the silicone material will stretch a great deal. Even if it is difficult, it should still be possible right? I just need the perfect adhesive for the job.
Where ever the balloon is bonded it will be thicker and therefore less stretchy. This will place great stress between the thick and thin areas even if they are molded as on piece. Silicone does not have good tear strength, so it does not make a great balloon material.
It would be the easiest solution to try first. Also be aware that it is also possible to use fabric reinforcement to get additional strength where/if needed. Knit fabrics have the ability to stretch.
Can you not overmold the TPE directly within the silicone mold, or vice versa? Can you design an interlocking (think multiple dovetail or keyhole slots) interface in one of the parts to increase the surface area of the bond line? If you are trying to bond to a part (sounds like you are purchasing the silicone bladder?) that you don't "own", you may want to, no really, you may need to, consider owning that mold tooling, even if it means you steal reverse engineer it. Then you can play with geometry, resin, surface finish, mold release, etc. etc. etc. to find what works.
Finally, as with any "how do I bond elastomers" question, I would refer you to the experts at Lord Chemicals,
