Even if it was somehow possible to scrape together enough negative mass to create a warp bubble and even if it was possible to exit that warp bubble at the destination, none of this addresses a much more fundamental problem. Any method of travelling between two points faster than the speed of light is literally equivalent to a method of travelling through time into your own local past and violating causality. There's no way around that, it's independent of the actual mechanism used to go FTL.

I think it's safe to say that warp drives are probably not possible. It's an extremely extraordinary claim. It's fine if the physicists want to keep tinkering away at it, but making any significant future plans or projections based on the assumption that they'll succeed is not a particularly good bet.