It's a porcelain toilet, right?
Metal screws come in a few varieties...sounds like they used Zinc-coated or low-quality stainless. It's possible that the chlorine in your water has actually caused the bolts to rust faster too since chlorine is caustic to steel.
You can get replacement tank bolts in a kit with new rubber gaskets. A new toilet costs $100-150 and up. If you're ok with the toilet, new hardware for the tank should be pretty cheap, not more than $10 and takes less time to install because you don't have to deal with your toilet flange and all that. Either way, you're going to deal with toilet water when you mess with it.
Here's a video on Korky replacement parts (since I don't know what brand of toilet/tank you have). Most big-box stores will have these kinds of parts and people there can help you. Just figure out how many bolts are in your tank, (2-4) and what brand it is. The bolts are used to compress a rubber gasket between the tank and the bowl to make that connection water-tight, but you don't want to overtighten the bolts.