Please advise about bleach damaged hair

Hello. I have chemical damage and am trying to work out how to handle my hair to direct dye my roots without breaking it at the damaged points. I'd be grateful for any help or ideas.

This is what I have done... I left a previous root bleach on too long. This was 8 weeks ago. My hair was pushed to the max but was OK. 2 weeks ago I did my roots again but, my hair is snapping at the overlapped point when wet. Last week I did an Aphogee 2 Step Treatment and Aphogee Balancing Moisturiser for the first time, followed by my usual deep conditioner mask (Shea Moisture Manuka Masque). I think it helped but it's still snapping when I've tested it at that weak point when wet. It seems reasonably strong when dry. I have not toned since the last bleach and it's yellow at the roots. It's not as light yellow as I would like it, as I washed the bleach off sooner than usual due to the snapping. It is a shade I can work with I think.

I usually dye my hair (without first toning) pastel purple/blue which fades to the lightest blue which is the colour I like it to be. I shampoo using Bleach London with added Manic Panic Violet Night dye. Then using my hands I apply a cheap conditioner/Violet Night mix to my hair, taking small chunks of hair at a time. I follow with a deep conditioner (Shea Moisture Manuka) under a cap for an hour.

My questions are about how to apply the dye, because if I do it when my hair is wet, after shampooing as usual, I am sure I will snap quite a bit of it. I basically don't want to be moving my hair while it's wet. I think I need to shampoo it before dying especially as the Aphogee treatment had silicone in it.

Would it work if I shampoo my hair then leave it to dry before applying the dye mix to the dry hair? My thinking is that when I apply the dye mix to my hair it will be dry and more robust. Then I'd make sure to move my hair as little as possible once it was applied and wet. Will the dye work on dry hair? Would it be better to include my heavier more costly conditioner in my dye mix so that it is dyed and conditioned in one stage to avoid having to agitate my hair when wet a second time?

Here's a bit about my hair and treatment in case it helps. Level 6, fine hairs, lots of them, slight wave, near hip length. All bleached, but pretty good condition except for this recent weak point. Washed with cleansing conditioner weekly (dry shampood after about day 4). Always dried naturally. Never heated (except for with the Aphogee treatment process). No silicone or other styling products. UV avoided. Smoothed into a scarf for sleeping. Shampooed only for bleaching and in preparation for colouring.

If you have any other ideas for processes which I may do to preserve my delicate hair while dying it, I'd like to hear them. Thank you for any help.