I agree with backofbeyond. It is a good idea to travel with a budget mindset, looking for cheap down-to-earth options, not overpaying for tourist traps and using your freedom of movement to go for unusual experiences. But setting your budget as your absolute priority will only lead you to spend your entire free time, and still quite a lot of money, on a camping trip where you see desolate forests and eat canned food from home.

There are ways to travel by bike on the cheap. Couchsurfing for example - I've stayed with CS hosts in Norway and Denmark, saving significant amounts of money. Another way is to go visit friends and stay on their couches. AirBnB and hostels are also often good options, especially if you are traveling outside of major cities and outside of peak tourist times - for example, all the accommodation in the Alps that caters to skiers in the winter will be very cheap in the summer, when you want to be there on your bike! (I paid twelve euros for a decent warm hostel bed - including free courtyard parking - at the Austria-Liechtenstein border.) And local hosts and other travelers you meet in hostel common rooms are usually the ones who give you the best experiences - because they are already in the mindset of sharing adventures.

By all means, keep your travel cheap and cheerful. But don't deny yourself the fullness of the experience just because you have a number in your head and you need to stick to it.