If the language is simple enough to be parsed with only regular expressions, then the language does not have context-free grammar, so bottom-up/top-down distinction does not apply. This also means that the language cannot have recursive productions, e.g. cannot support expressions.

But it depends on how the list of regexes is used. If it is used as part of a recursive paring routine, then it is a recursive-descent parser where lexing and parsing happens in the same pass.