Beet pulp can expand quite a bit
You are supposed to weigh it dry, but don't feel compelled to feed 1-2 lbs of it just because the bag says so. It's not like a fortified ration where you want to make sure your horse is getting enough nutrition; beet pulp itself isn't super rich in nutrients. It's mainly fed for its highly digestible fiber.
My barn makes a big batch of mash each night with 4:1 beet pulp and rice bran, soaked for 3-4 hours. Not all horses get the same amount of it, but most get 1/2 to 1 scoop using a 5-pint feed scoop. If I had to guess I'd say it's probably somewhere between 1/3 and 1/2 lb equivalent dry weight per scoop once it's all soaked up.