Washing a dog with a bum back leg (and tick/flea question)

My houseguest 'til Monday has a bum back leg. (This is new, she was fine a few weeks ago when I last saw her.) She also has a good funk about her and is a few shades darker than I remember her being. She needs a bath. The downstairs bath has a walk-in shower where I could use nice warm water, get in there with her, and all that jazz.

I have two concerns:

1) Would this be safe for her? I don't know if she's ever had a bath (though when I first saw her she was really fluffy and lovely) and she's a herding mix so could be little tightly wound I think. If she tries to bolt on the slippery tile I'm worried about her falling and getting hurt.

2) I gave her Capstar today and was told that Capstar does nothing for ticks. This shower will be where my mother will bathe when she comes in a little over a week. So you think that 24 or less is enough for the Capstar to have an effect on the fleas and do you think that one bath there could result in problems for my mom?

Suggestions from the wiser and more experienced?