So there is a lot to unpack here:
1st point:
While we don't know the exact number of senate seats during the Republic (Prequel Trilogy) we can make a safe assumption using this image that it is more than 1000:
I don't have the source, but I've seen it referenced many times that there were approximately 10,000 "Jedi" during the Prequel trilogy. This includes Youngling and Padawans. It's worth noting that in Attack of the Clones, over 200 Jedi were there for the battle, and roughly 30 lived.
This means once the clone wars actually started, the Jedi Knights and Masters were already thinned out.
2nd point: The Jedi seem to favor the republic, and let the Outer rim take care of itself, and obviously had very little presence on Separatist planets. So basically, if you weren't born on a planet that had representation in the republic, then chances are you never saw a Jedi. Sometimes even being on a Republic planet still meant you didn't see Jedi, or if you did, it was common for them to simply say "Jedi Business" and you left them alone. You see this several times in the Clone Wars series, even on the lower levels of Coruscant. On top of this, planets that were safely inside the Inner Core of the Republic, and never saw battle of the Clone Wars, also likely never dealt with Jedi.
3rd point: Propaganda. The winners of war get to write history as they see fit. The Empire began teaching that Mace Windu led an insurgent group to kill the Chancellor/Emperor, but were thwarted by the Clone Army. While this point isn't seen in the movies, it is mentioned in the Lost Stars Novel.
4th point: It's estimated roughly 100 Jedi survived the Purge. We know at least 10 of them became Inquisitors. Vader hunted down quite a few himself. In the end you're looking at probably 40-60 Jedi, who are deep enough into hiding that they dare not reveal themselves spread across 1000s of planets.
If we assume there are 3000 planets in the Galaxy and 50 living Jedi, the odds of a Jedi being on your planet is 1%, and then the odds of you coming across that Jedi on your planet become drastically lower considering how reclusive they will have become.