What is expected from a mathematics student bachelor's thesis?
What is expected varies dramatically between different schools. In my experience, bachelor's projects in math can vary from trivial to nontrivial, and also from expository to original research, and the two scales are somewhat independent.  I have supervised both trivial and nontrivial expository papers, as well as several undergraduate original research projects. 

The concerns you have about being able to do research are common, but they are somewhat misplaced. You can almost certainly do more research than you believe you can do. 

Here is an anecdote. In the 1980s, U.S. math departments began to offer "Research Opportunities for Undergraduates" (REUs), summer programs for undergrads to work on research. At the time, these were viewed very skeptically by many mathematicians. I have heard personal anecdotes that the NSF and NSA gave out a few initial grants on a purely experimental basis, not expecting to see very good results. But the projects flourished! Now there are many math REUs, and grants that allow schools to offer them are very competitive. The math community went from doubting that undergraduate research was possible to embracing it. Many math faculty are now required, or at least strongly encouraged, to mentor in undergraduate research if they expect to get tenure. See "Undergraduate Research
in Mathematics Has Come
of Age" from Notices of the AMS, 2014. 

The key thing is to find a good project - which means finding a good advisor. Your advisor is responsible for finding a question that is accessible to you, for pointing out the background that you need to learn, and for mentoring you as you go. You still need to work on the research - we won't do it for you - but we don't expect you to operate as if you have already earned a PhD.