How do I access the secret room with loads of coins?

I am the OP. I got to the same room again, and I was doing particularly bad that run, having hit into many obstacles, so I know that it's not a reward for having been particularly fast. Both this time and the previous the cave appeared around 5 km in.

In the cave there is a point where you can go right or left. Depending on whch wayy you turn, you go into the coin room. I believe it is the right turn. Sometimes it helps to just go slow in some areas. You will lose time and the game quickly but it is these dry runs where you can see what you miss at high speeds. Slow down and see sme of the turns, shortcuts, etc.

Take out the bone in the middle of the cave opens the secret room

This is a complete random event, I have found it while avoiding every obsticle, while hitting some stuff, and while taking out just about everything.

Also there's no way to avoid it, it is part of the course, turning left or right do nothing to help or no chance in missing it.

All segments are randomly assembled as you play. You will notice some recurring segments, with time they'll become familiar and you'll know, to a degree, what's coming next, but the order in which the segments are presented is random.
Some segments, (like the treasure room, the arctic scene or the volcano) are more rare then others, therefore there must be some form of "ranking" in the randomness, but the tracks are generated at random.

I think I might have found out the way to that secret room but I have TWO Theories because I got in 2 times in 2 different runs ... I was just playing it and I broke all the 3 relics of each stage I.e "the surf boards of the beach, the crocs of the swamp and the idols of the cave" and I got into the bonus room ... And the other way I got in was I drove through the swamp into the cave and broke the very first idol on the left side after entering into the cave and the magic doors appeared out of nowhere !

I got into that room many times . And each time was different from the other . It appeared that there was no role .. No matter how you play or which direction you follow .. You just enter it in a random way

It is random. However, do FOUR things when you see the double gates with the wall torches (which means it's coming up): (I) makesure to grab the magnet, (ii) as soon as you hit the magnet, turn left because you hit a bump that send you airborne into the cave wall; by turning left, you align yourself to land right in the middle going into the coin room, (iii) tap the brakes intermittently to grab EVERY coin; if not, you'll drive by a lot of the and miss the ones on the edges, and (iv) just as you leave the room, get ready to grab the coin bubble as you leave (and hopefully you have it up to 500 coins)