First of all to limit damage I'd say go for colour b4. In fact the decolour version (newer one) is said to better. Go for the "extra" version, for more lift.
The only problem is you can't redye for a few days - you need to use a 6-8 washes colour in between if you have a dodgy result between removing and redying.
Red is hard to get out, even with bleach.
I've done it loads, and red is a pain. It also depends on what colour you used - if you used a silicone based colour like XXL, then that colour causes silicone damage the minute you use straightners after it!
You said you bought another bleach in case its not light enough - DONT use it after the first bleach for several weeks - you could land up with serious hair damage by double processing (triple processing once you colour!)
If you do go down the bleach route
*cover your hair in pure coconut oil for at least an hour before. This helps damage limitation. Dont wash it off, just apply the BBlonde on top. Make sure you've got plenty for long hair - you dont want a patchy result.
*If you get light enough - use a semi-permanent (up to 24 washes) Contrary to the name, they are very much permanent. "Permanent" dyes are very unnecessary unless you are dying over grey hair.
I only learnt the above about two years ago - believe me I am not kind to my hair!
but following those tips can really make all the difference. I went from black in April to pink and it took several months and patience, but it wasnt worth risking my hair going chewing gummy and looking rough!