In direct competition between wrestlers and jiu jitsu players, you run into the problem of differences in rule sets. For example:
- Jiu jitsu players do not consider back exposure alone to be bad position and will very commonly attack from positions with back exposure. The guard position is a scoring position for the top player in wrestling if there is back exposure for the player on the bottom.
- Hyperextending an opponent's arm is not allowed in wrestling.
- In wrestling, stalling is a penalty. In jiu jitsu, players may make very slow progress that would probably be called stalling.
Because of these differences, it does not really make sense to have direct competition between wresting and jiu jitsu. You have to choose one or the other, or create modified rules to compete against each other.
In the US, cross training in wrestling and jiu jitsu is not unusual because wrestling is a common sport offering in secondary schools and jiu jitsu is not. Many students will compete at their schools in wrestling and do jiu jitsu on the side or in the off season.
If you are interested in experiencing new situations for application to wrestling, my advice is twofold:
If you are just interested in improving your wrestling, the simplest thing you can do is travel to tournaments or training camps, or practice with people who do. Martial arts have a huge range of possibilities, and every coach/teacher may specialize in different techniques. Go see what is out there and how others wrestle. Practice with as many different people as you can find.
This will be a much faster way of improving your wrestling than trying to take jiu jitsu and squish it into the wrestling ruleset.
If you are interested in studying some jiu jitsu, find a jiu jitsu school or some friends who practice jiu jitsu and join. How this may improve your wrestling may not be obvious for some time because many techniques will not be directly usable in wrestling. I estimate the payoff time on this kind of cross training study to be 6+ months, and you also have to factor in your lost wrestling training time.
Don't assume you know in advance what you will be learning. If you already knew, you wouldn't need to attend the school.