When you think of growing bitcoin safely, you get very few possibilities. Also it needs long time to grow compared to the methods which involves high risk factors. Upon ones need can decide which method to be chosen for growing hard earned bitcoin.
Well, if it is for safety, then it will not be fast.. I think OP must be thinking of something like a bank that gives only small interest in a month or year.. .01 as capital I think is small, but he could try to make a research about gambling sites, there are gambling house that accepts small investments, only that it's a bit risky.