Is this a good way to bath a Stray cat?

I've been feeding a stray cat in my neighbourhood which is very dirty. Her fur is very long and although she's grooming herself, she remains VERY dirty. When I say very, she is definitely in a need of bath.  The problem is that the stray cat is still a bit scared, she allows me to touch her, but when she hears a sudden sound, she runs away. If I bath her normally I'm definitely going to get scratched and noticing her claws, I'll get  a lot of deep scratches. So is there any way I can trap her in a shopping basket, apply soap from the holes and then gently use the garden hose to bath her? I mean, will she panic a lot and injure herself and will it cause her a traumatic experience? If not, after the bath, for how long should I leave her in the basket?((The basket has holes so there's no way she can drown)). If harms her, do you know another way to bath her without risking to get scratched ?

PS - I want to bath her because I want to move her in my enclosed space where my other two cats live. Winter has already started and in my country the rains have already begun and I'm pretty  sure it'll snow and the cat will find it difficult to survive. Thanks in advance.

I would instead take her to the vet for a check up.  You want to be sure she is spayed as well as disease free to be around your other cats.  While at the vet, you can ask them to clean her up a bit.  Most vets will help you out in this situation.

I agree with Shadow. I would advise against attempting to bathe her at this point, especially the way you describe with the shopping basket. Being trapped inside while hose water is coming down on her will scare her badly and possibly destroy the trust she has in you. There are cleansing cloths you can buy in any pet store that don't require water, so maybe when she's more comfortable with being touched you can gently rub her clean with those. The only times I've ever bathed any of my cats have been when they've had bad diarrhea I can't remove from long fur, or have peed in the carrier, and then those are only half baths. It's wonderful that you're going to help this cat.

If you have her spayed, you can ask if they could give her a shave-down during surgery. I think most vets would at least shave out mats. What country are you living in?