Quests are an excellent way to earn BrickBux, as each gives 500 on completion and some can be completed in less than 30s

Are not worth it as the payout is too low.
Don't do this for farming (unless you really like exploring)

Highest pay out per Race is A Class. (Level 20+)
The amount depends on the type.
Highest ist Sky Cup, then Grand Brick Arena's and then the normal races.

Obviously the issue with the above is that replaying a race in the same class significantly reduces the payout.
The Sky Cup goes from over 3K for completing to 125 (seriously).

Might sound extremely boring, but by restarting the game you reset the amount of money earned.
On PC the save location is
(You can copy this in your explorer window or use Win + R)

Simply close the game, rename
to something else (to keep your old save), and start the game.
Once you start the game again you will be greeted being able to start a new game. (If you did not delete the other files in the directory, you can use the cars you built before)

Aren't there faster options?
Of course - if you think "savescumming" is an option, you can simply make a backup of your save before you start a high value race, such as the Sky Cup.
After you earned your 3K for completing it, you can simply quit the game and "reload" the savegame from before.
You are now able to replay the Sky Cup for the full reward.

Alternatively, if you completed all Quests, you get 2000 BrickBux extra.
By keeping a Quest that's fast to complete for last, you can make a copy of your savefile before you finish the last Quest.
After completing the last Quest (if you pick one you are fast at, you can easily do this in 30s), you will earn 500 for the quest and 2000 for "Questmaster" (completing all Quests)
You can now reload the save again and repeat. This process can yield around 2500 per minute (might be boring though)