It depends. As is pretty much always the case.
With today's manufacturing and QA possibilities available, I guess it's quite hard to build a truly terrible "basic" bass guitar nowadays.
So to answer the sub-1000 challenge, first thing is to decide on the features you'd like to see in the bass guitar. 4 strings? 5 strings? 6 strings? Active or passive? How many pickups? Do you need LED in your fingerboard, or detuning keys? Lefty? The combination of features you'd like to compare between the "cheap" and "expensive" basses can make such a comparison impossible from the get-go.
Then, there's the options thing. What kind of finish? What sort of tuners? Relic'd? Zero fret? Alternate strap lugs position? Different pickups? Preferred neck profile? This will drive up the possible price range, too.
You will be hard-pressed to find a sub $1000 e.g. 5 string bass with LEDs, two active pickups and electronics, plus a piezo, fanned frets, string-through, and custom paint job that puts a $2000+ bass with the same specs to shame – to be able to build such an instrument for $1000 or less, they'd need to cut corners e.g. at QA or wood and electronics quality. Things might look differently though if you're just after a 4 string P-style bass with one passive pickup, standard neck profile, and a "don't care what it looks like, if it's too ugly I can strip it and repaint it myself" finish.
Proper setup and professional fret-dressing can turn a cheap "simple" bass up a notch or two, too, anyways. And you'd still be way below the upper $2000+ starting point. Swapping out the pickup and/or hardware probably would also be possible inside the budget, if so desired. But retrofitting the cheaper bass with LED, or a professional paint job in your preferred colours and pattern etc., plus a different neck, less so.