Bulk wine isn’t quite what it sounds like (you’re not buying wine in bulk, the industry calls that "by the case.") Instead, bulk wine is an industry term that refers to something akin to "private label." The brand on the bottle of the wine is not the same the winemaker or winery who produced it or the vineyard that grew the grapes. Sometimes this leads to inferior quality, but often it doesn’t.
In France, there is a concept of a négociant who gathers grapes and wines from local producers and gets them to market under their own name (like Louis Jadot and Joseph Drouhin). In the US, we don’t have a formal role like this, but you probably know of some brands that employ this business model: Cameron Hughes Wines, Kirkland Wines (from Costco), and 90+ Cellars are the most well-known.
Among wine clubs, TastingRoom.com, Bright Cellars, and Vinesse all use the négociant model to bring wine to market more affordably than they might otherwise be able to. Some people think that Winc, Firstleaf, and Nakedwines.com sell bulk wine, but they do not — these are wineries in their own right and produce wine under their own labels (well sort of, Firstleaf is owned by Penrose Hill which produces its wine).