hi there amyamanda! welcome to the world of no running water. it's not as bad as others can make it sound. in fact, your bathing ritual can be quite enjoyable.
i have no tub or shower, either, but i have an enormous farmhouse sink with a drainboard. to be honest, i sometimes move the dish drainer away and sit on the drainboard for a quick wash-off. if you don't have a similarly sized sink, this probably won't work for you. but i have the long-bathing method also, which goes like so:
wait 'til night, when the kids won't interrupt me.
my kitchen sink and woodstove are near each other, with a sizable drainboard to set things on, so i work in this area.
fire up the woodstove. it's nice to have a warm room, and though this isn't essential, it's a nice place to keep extra water heating. light candles for ambiance.
draw up a dining room chair and a galvanized tub - set the tub at the foot of the chair. drape the chair with a terry robe or a towel to sit on.
heat up a gallon of water and mix with cold to get a couple of gallons of warmer-than comfy (it will cool as you go) water in a dishpan. set that on a nearby counter or table with two washcloths - one for soap, one for rinsing. a pitcher or an empty yogurt tub or something like that to pour water over yourself with may be nice too, depending on how you like to do things.
get a fluffy towel, or two if you'll do your hair. if i had wood flooring or similar, i'd put dry unclean towels (from previous baths) under the tub, or if like me you have flooring that can get wet, you can wipe up escaped water with your used bath towel once you're done.
start at the top and work down; that way, you're never rinsing over something you just washed.
i wash my hair in the kitchen sink, using pitchers of water (or the kettle) to pour with. wet, lather, rinse. wrap hair in towel. it doesn't take as much water as you'd think, but the better you get at it, the less water it'll take.
next i lather up one washcloth and soak the other in plain water. (i'm always working next to the sink for my convenience setting down washcloths and so on.) wet face with one, soap and scrub with the other, rinse with the first again, and dry with the second towel, or if the one from your hair is long enough, the tail of that one. all that i do standing at the sink.
now i'll open the terry robe (or a towel) over the chair to have somewhere cozy to sit later. standing feet in the tub, within reach of the dishpan of warm water (adding more after the hair/face routine if needed) i start working down - wet, soap, rinse (with washcloth and then pitcher) and dry. the torso is one area, the behind and goodies another, and then i sit to do legs and feet. if you don't have a stove, drying as you go keeps you much warmer, too. when you're down to the legs, you can put your arms through the sleeves of your terry robe, even, kick back and take it easy.
by the time you get down to feet, they'll have been soaked nicely and can be paid attention to. much nicer than in a shower, where they tend to get ignored. here i scrub at them with an exfoliator thingy, wash, dry, clip nails, and apply lotion.
after you get the hang of it, it feels rather more civilized than either being blasted like a firehose with water from a wall fitting *or* soaking in your own dirty water in the tub. at least, i like to look at certain things as benefits rather than hardships. and it really is quite nice. also, the sofa isn't far from the woodstove, so if DH is up reading, he gets a show.
make up your own ritual - it's very nice to take time with this, i feel so pampered when it's over.
a few notes on soaping:
it took a while to realize i didn't have to soap everything, then rinse everything, in that order. going in stages is much nicer, and drying as you go keeps you warmer.
if you're using water from a rain barrel, plan to use less soap. this water is so much softer that what i was used to before, i didn't know why it was taking so long to rinse.
use an eco-friendly soap like bronner's, especially if your greywater goes to the garden or something. bronner's makes an unscented baby-mild one that i quite like. it's even quite good on hair.
get a big enough galvanized tub that you feel you can move. i tried to start with a smaller one, but soon realized that size didn't matter because i could keep it outside. (in my small house, storage space is a premium.)
everything you'll want to have, keep handy. this seems basic, i know, but when i started i kept forgetting things and having to get up, and now i just keep it all in the kitchen instead of the WC. there was no logical reason to keep things there, anyway. now i store toilet paper and rags and cleaning supplies in the WC instead. (i guess it's not really a 'water closet' as it's a water-free composting toilet, but you get the idea.)
live and learn!