How much Beet Pulp

You can feed up to 50% of her forage intake of beet pulp a day safely, so don't worry about feeding her too much! When I feed it to put weight on, I start with TWO (2) 2 qt feed scoops of SHREDDED beet pulp. Add that to a big flat backed bucket. Put enough water in it to just come up to the top of the beet pulp. Let that soak for 20 minutes. You should end up with the bucket about 3/4th the way full of beet pulp. Pour off any excess water, then add your ration balancer.

If she doesn't eat all of it, then back it down to one (1) 2qt feed scoop of shredded beet pulp.

If you can't get shreds and only have access to pellets, then reduce it to 1 scoop or 1/2 scoop. It's more densely packed, so it will expand more when you soak it. You also need to soak it for 45-60 minutes to get full expansion, or longer if the water is really cold.

That said, you do not NEED to soak beet pulp. As long as your horse doesn't bolt her feed down, feeding it dry is fine. Just make sure she has access to plenty of water.

I would also add a fat source like corn oil or whole flax seeds (both affordable). You can feed up to 2 cups of oil, though 1 cup works well. Start with just 1/4 cup though and work your way up, as some horses don't like oily feed. Feed 1-2 cups of whole flax. Your feed store should be able to order you 50 lb sacks of flax if they don't already carry it.

Here is a great article by a animal nutritionist about Beet Pulp.
Should answer any questions you have.

The Myths and Reality of Beet Pulp - Susan Evans Garlinghouse

You should not feed beet pulp in excess of 40% of the horse's roughage.

So if the horse is getting 15 lbs of roughage per day, (or 1.5% of it's body weight), no more than 6 pounds should be beet pulp

You can start off with 1-3 cups and increase from there

In my opinion beet pulp and minis do not mix well. I have seen to many minis ruined on beet pulp, because the necks get big and you can't get it off even with sweating. I would not feed beet pulp to any halter minis. Now with that being said, no flaming please. I do know many big show farms that swear by beet pulp, and highly recommend it. I think it does depend on the horse, for me I have not had the best experiences with beet pulp and keeping the necks trim on my horses. I do keep beet pulp on hand, but only use it on a last resort basis.
I have used it on the large horses with great success, just not so much luck with the minis.