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):
Therefore, it should be 0-based and half-open.
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Please define "file convention". Are you talking about 0/1-based start coordinates?
Re Neilfws: Yes, you are right.