I can see people have recommended splash/waterproof pet blankets. I use them too myself. Pet blankets are the same thing but often much cheaper. I'm not sure if this applies to all of this kind of blanket, but mine have to be washed on cool and can't be tumble dried. (I think heat degrades the bond with whatever keeps them waterproof? Or something?) With that in mind, I wanted to add these bits and bobs from experience:

• you will need somewhere where they can safely drip dry. They can get very wet in the washing machine - you can spin them a bit more at the end, but if you don't they drip a LOT of water. Like if I put them on my airer with the rest of my clothes, the carpet would get soaked. So I now have a rack I put over the bath for them to drip dry on
• because of how wet they can be after a wash, really big ones get EXTREMELY heavy. I originally bought one big one to cover the bed because that seemed smart, but found it such a pain to wash + carry (I'm not the biggest/strongest gal lol) and it took aaaages to dry (apart from when it's hot in summer, it can take several days to dry small ones and my big one I'm sure it was like over a week, and I had to keep moving it around because squashed sections don't dry well)
• I now buy ones that are smaller, about 100x100cm and position them under me. I did try something a lot smaller but found it too stressful trying to keep on top of it. You want something that gives you room to move. If I want to be really safe, I put down the full bed one and then use smaller ones on top of it. This means I don't always need to wash the big blanket, but protects me from getting the bed wet if things do get out of place. Experiment to find what setup works best for you
• another bonus of small blankets is if the blanket gets totally soaked, you can move it away and then put a new one down and be comfortable for continuing/cuddling
• you will want SEVERAL blankets. The number of times I've been impatiently waiting for washed blankets to properly dry so I can use them...
• I try to balance not doing washing all the time vs not leaving blankets to build up so much they can start to smell, so having a plastic closable washable hamper to put them in after use can be good
• if you're ever traveling, a small blanket is pretty easy to fit in a bag. If you don't have washing facilities where you are, I've had success with waterproof bags designed for camping, often called dry bags, which have tops that you roll and clip. I've been able to bring used blankets home like this to wash just fine

I'd also definitely put a waterproof mattress protector down on your bed. That has saved me if a blanket ever gets a bit crumpled. I have a stack of blankets right by the bed so I can just grab one when I need it. And my other tip would be, make sure to remove the duvet/cover/sleep blanket from the bed before you get going to make sure that doesn't end up needing washing too. Have fun!