How can I protect twine from water?

There are several ways to water proof paper.... these should work for twine. One is with wax.... so coat it with wax, one is with an alum mixture. See Wiki How.... there is an article about this. Hope that helps a little! Love the Light fixture idea! Hope they turn out great.

You can always coat it in vaseoline.

Spray on several light coats of a good quality spray lacquer (Minwax or Rustoleum are both good). The lacquer will protect the twine from moisture and, unlike wax, will allow you to clean off the dust. Good luck!

Or paint it with polyurethane.

Good ole varnish/polyurethane. Most of my outdoor items ranging from furniture to decor get a coat of varnish. Protects from the humidity of the south, resists mold mildew. I have wood furniture on my covered porch, at least four years, and i would not hesitate ro use in my home today. Cannot imagine it would not be applicable to your bathroom. Good luck.

Spray it repeatedly with several light coats of some sort of oil-based spray paint (even if it's clear, it needs to be oil based). Once you are really feeling like it is well coated, maybe even consider dipping the whole thing into a bucket of polyurethane and then hanging it somewhere (NOT over anything you like and preferably outdoors) to dry thoroughly. I would probably make a second, smaller one to test the polyurethane dipping idea before doing it to the one I like since it is a guess on my part, not the voice of experience.

Thank you all! I didnt even think of using a varnish- off to do that right now!

Nice Job Wendy! Excepting when it merited Enamel or Acrylic Paint, [For Stencilled Designs] I used to use a brush-on lacquer on my client's professional displays, effects and Shades, and did that brush-on after the ballon slightly deflated, [relies on weather, not any to the minute timetable] but Varnish or Polyurethane will do too.

Bear in mind, you need to wash it inside and out after it dries, otherwise flammable residues may yet reside on the product.

As you already removed the balloon, You may need to blow up another balloon inside, to protect the design from deformation if you are brushing or Dipping, rather than spraying.

Also, because the Diameter is really small for a 100W or higher bulb [>2.3 inches per 10 Watts is Diameter Recommendation for any Paper or Twine Shade, with Incandescent Bulbs, for example: 75 watt bulbs need a 17.5 inch diameter, 25 watt bulbs need 5.75 inch Diameter, Small 5 watt Bulbs from christmas lights need about 1.25 inch diameter], you should reduce the Wattage on that incandescent bulb or get yourself a Cool Led Bulb, CFL Flourescent, or a Dimmer Switch, [Knob or Slider] if you intend to persist using the incandescent [hot tungsten] bulbs.

Edit: Also you can use FlexSeal Clear...

Maybe she waterproofing spray!?