Scope adjustment

Don't think we have boar in New England. Did you mean bear sighted?

BORE sighting has also been found beneficial.
 
First of all, at what distance do you want to have the bullet's point of impact coincide with your point of aim.

Without knowing that, it is impossible to diagnose the problem.
 
At five feet from the target it's hitting 6" too high. This is with the elevation adjusted to the max.

I probably want to sight it in for +-30 to 50 yds ? I don't know the tragectory of a 22lr and at what point it starts to drop. This is just a plinker gun.
 
I bought an inexpensive BSA R3-7x20 scope for my Mossberg 22 rifle.

I don't intend to be glib but I don't think the price point of $24.95 will get you a good 'scope. (Even for a "plinker".)

You might want to pick the collective brains of NES with a "What scope for my .22 ?" thread.
 
20" high at 30yds is a lot. Is the mounting system correct for the rifle? Some have different mounts for the front and rear because of height differences.
 
At five feet from the target it's hitting 6" too high. This is with the elevation adjusted to the max.

I probably want to sight it in for +-30 to 50 yds ? I don't know the tragectory of a 22lr and at what point it starts to drop. This is just a plinker gun.

Don't take this the wrong way but you need to admit you don't really understand what's going on here. This: "I probably want to sight it in for +-30 to 50 yds ?" is indicative of that. You can sight in a rifle for only ONE distance and from then on you have to adjust your sights up or down (either using the adjustments or by holding off) depending on the actual distance to target.

Here's my advice to you:

1) Buy a better scope. Optical instruments (and that's what telescopic gunsights are) are one of the few remaining products where you DO get what you pay for. Plinking is fun and it is hard to have fun when your sights do not do what they are supposed to do. Ask for advice on what to buy and do not be surprised when you find out that it may take more $ than what you have in the rifle itself to get a good sight.

2) Get someone from this forum to meet with you and get you some coaching on the basics of bullet trajectory, bore sighting, and sight adjustments.

I would personally love to help you and coach you if you and I lived closer. But there are quite a few experienced riflemen in this forum that can help you as well or better than I.
 
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