Rosa,
Sadly, corruption is alive and well in most of Latin America ... it's endemic to the culture, from highest to lowest levels of institutions. It's how business is done. Sorry, that's the reality in many situations.
Could a tourist get busted for offering a bribe? Absolutely. But it all depends how the little drama plays out and depends on both parties coming to an agreement. Most times everybody is happy ... and you continue on your trip.
To the OP:
Yes, you can buy a bike in Colombia, then travel to all the countries in the area and cross borders.
If you go through proper procedures when buying (most dealers can help you with this), you will get a title in your name for your bike. So with this, you can travel anywhere. You should always buy insurance for EACH country you visit.
It is required.
But as stated ... selling is technically ILLEGAL in ALL Latin American countries outside of Colombia. You and your bike are in a country as a guest and your bike is on a temporary import permit.
You have a time limit and are supposed leave the country with your bike and to Cancel your TVIP upon exit.
So, your options could be:
Do a BIG LOOP and circle back and end up back in Colombia and sell your bikes there.
Find someone in Bolivia who is not concerned that the bike is of Colombian origin and is willing to take that chance. Of course, in this case the price will be well below market value in most cases.
Local bikes shops, indy mechanics and dealers may be willing to buy your bike.
But you may not, in future be able to enter Bolivia with a vehicle or would have to pay fines for leaving without canceling your TVIP. You, yourself will face no such restriction, only any bike you're riding.
Lots here on HUBB all about this. I suggest taking a day or two and READ UP on these subjects. Many good threads and posts.
While Bribes can sometimes solve a problem or get you out of trouble, they can't always be applied in all situations. It can also take an artful application of diplomacy to "make a deal" with an official on the spot. Not always easy.
Certain situations will preclude any sort of Bribery going on, and in this case, you could end up in jail if not careful. So tread lightly in this area.
But suffice to say, anything is possible.
Try to keep it all legal ... learn as much as you can here on HUBB. It's all here.