there are additional options
its like in your country Scotland. You need to be registered as a foreigner with a permanent visa, address etc. Please check out the English dependence of the Peru embassy for the details how to immigrate to Peru, its not so hard if you have cash.
Now, as in Scotland, you could do the following: Find a local that has a bike (the one you bought) and gives it speaking lends it to you. The bike has then a Peruvian registration, Peruvian insurance etc. You will then need a paper from that local friend that states that he has allowed you to use it and cross boarders (otherwise everybody will think you stole it...). And then you can cross with that bike and registration the boarders using your passports etc. Then the local import rules apply, most likely you will need to take the bike back to Peru.
Please search the HUBB for more Threads.
Hope that helps.