This is a tricky question, but when I look at it from the opposite direction, I think it makes sense to say it's a bull as long as it remains flat.
If it were a bear, and the market remained flat at the bottom, I think people would still consider that we're in a bear market until it recovered.
The more interesting hypothetical, however, I think would be at what point do we consider a recession risk has passed? If we have flat markets for a year, two, three? Is that equivalent to bypassing our traditonal ~7 year market cycle? Lots of people think we're overdue for a recession, but if the market goes sideways for an extended period of time, isn't that essentially accomplishing the same thing?