Doesn’t have to be all at once. Do a little but at a time throughout the day

I had to force feed my rabbits water (and pellet sludge stuff) before because of GI problems

So basically though just get her in a comfortable place where she can’t back up or run away ( maybe between your legs sitting criss crossed or with the help of someone to hold her still?

Then stick the syringe in her mouth of to the side a bit but like, in her mouth still

And shoot down a bit of water at a time, very slowly, if she even swallows half of it your making process, if it’s in enough (but not to far so you don’t choke her) she’ll basically have no choice but to swollen since rabbits aren’t very good at spitting out

So not directly towards the back of her mouth and don’t push in very much at a time, and push in very slowly. (Don’t shoot in fast cause this could choke her too)

And you should be fine

And I’d listen to your vet because they peobably know more about the buns condition plus more water will just make more pee if there isn’t anything wrong so you should try anyways

Any chance you can upload a pic of the reddish pee you are seeing? Do you see the pee right after she does it or find it later on. (Pee turns darker colour once exposed to the air.

If you are having real difficulty getting the additional fluids into her, talk to your vet about giving her subcutaneous fluids at home instead.
Did much sludge come out when her bladder was expressed?

I second listening to your vet!

In terms of getting water into your bun, Vanessa (another BB member) has been able to get her bun to drink a lot of water by adding a tiny amount of apple juice to it. You could also try mixing in a small amount canned pumpkin. You might try offering that, and see what happens. Also feed her greens dripping wet, and be sure that water is offered in a bowl or crock, rather than a bottle. 

What veggies are you currently feeding? That information might help us determine why the sludge happened in the first place, and if there is a dietary reason for the red pee. My buns only get red urine when I feed them beet tops or red stem chard. 

Does she eat pellets? Have you tried adding water to her pellets and letting them soak so it’s like a porridge? That would help get some water in her.