To get dog hair off of bedding put on some rubber gloves and rub the glove across the fur which will help lift the fur up off the bedding and then it should be able to be raked into a ball which you can then easily lift off the bed.
You may also need to use a pet hair rake or comb to work the dog hair out of the bedding.
You can also use a lint roller to help get dog hair and other hair off of bedding.
Then after you get the most of the hair off use a vacuum cleaner to suck up any leftover hair and then put the bedding in the washing machine.
You just want to get most of the dog hair off the bedding before washing it.
The washing machine should take the last of the dog hair off the bedding once you get the majority of it.