First, the technical answer (if it's boring or you don't understand, just skip to the practical part):
Actually, there may be some confusion involved here. Under the standard interpretation of the mathematical operator "/", the operator is "undefined" for 0. What this means is that the operator denotes a "partial" function which is not defined for every input.
There could be systems in which division by 0 results in "infinity," but this would be a non-standard system. (Although in the most popular non-standard system, based on infinitesimals and transfinite cardinals, division by zero is still undefined.)
Wikipedia has a nice article that goes through some possibilities, including the idea that division by zero results in infinity.
"#DIV/0!" is not strictly a bug, it was intentional. This is Excel's way of saying "undefined," but there may be a way to get a different result. One solution might be to write a macro which scans the Excel worksheet either for "#DIV/0!" or for formulae which actually divide by zero, and then overwrites these entries with something more meaningful (for example "infinity"). There may be other ways, but that is the one that comes to mind.