Because bigWig is binary, you perhaps do not need to worry about its internal indexing. However, when converted back to something human-readable, like bed (0-based, half-open) or wig (1-based, closed), you might rely on that format's particular indexing scheme.

This is not a stupid question, by the way. Indexing is important to get right in bioinformatics (and in general applications of computer science).

I have looked the BigWig paper, the supplement data shows that the BigWig stores chromStart and chromEnd as followings (Supplemental Table 13):

1. chromStart: Start position (starting with 0).
2. chromEnd: End of item. Same as chromStart + itemSize in bases.

Therefore, it should be 0-based and half-open.