If you have the "poder" or power of attorney over the bike then you have the right to leave the country with it regardless of whose name is on the TIP. I've done it twice in the past year no problems. When you enter the next country (Chile for example) the new TIP will be made in your name, it's really that simple.

I think people make up scare horror stories about travelling with Poder. It's nonsense, if you have a poder made by a genuine notary and apostilled by the ministry YOU WILL HAVE NO PROBLEMS. Other than 1 border that I know of at the coast in Peru to Ecuador where they don't accept vehicles which aren't titled to the owner. I crossed at the inland border here to avoid it.

A tip for you though, as I've bought a Colombian bike from a different country before. As well as the Poder, download from the Colombian SIM website the documents for ownership transfer and have the original owner sign and fingerprint them. Also download a "contrato compra venta" and fill that out, and have the owner sign and fingerprint it too. This will save you A LOT of hassle when you get to Colombia.

Also, the Poder: try to make it a PODER ILIMITADO. And also make sure (100% SURE) that you get the Poder apostilled by the ministry of foreign affairs (ministerio de relaciones exteriores). Otherwise the Poder will not be valid for anything.