I am currently an MSc student in math in Europe (I'm doing mainly analysis and applied math). During my Bachelor's I've had mainly average grades (I'm not sure what the exact GPA equivalent is, but it would be around 2.5, I guess). Now, in Master's, I've been getting only good grades and I am looking forward to finishing with distinction/honors.
My first PhD option would be at the university I have been studying in the last few years, which is good and well-known, but below the ones in the US or the top unis in the UK. Some of the programs are funded, depending on the advisor. How important are my Bachelor's grades? Am I overestimating myself if I go and talk to a possible PhD advisor and, moreover, ask him if I can enroll on a paid PhD program?