The bucket will work for mead just like any other bucket will, the problem is that you're going to have plastic bucket flavored mead. Food grade plastic is what you need. Please don't try to cut corners by using a plastic container that is not food rated, you'll be VERY disappointed, and we'll keep tooling on you about it until you get something appropriate for meadmaking.
A lot of people are tight on cash, I've found myself in the same situation more than once in my life. But, there are some things that do not bear cutting corners, mead making is one of them. Sure you can go and get a plastic one gallon milk jug, and ballon, some bread yeast and Costco honey and make a passable mead. But don't expect that it will be great, or even good if you don't put in the time, use appropriate equipment and give it the time it needs to develop. This is not an inexpensive hobby, nor is it one that you will be able to get instant gratification.
Bottom line is that you can't make great mead from bad ingredients and equipment.
Oskaar <--- Steps off soapbox