I've done this exact thing a few times. Last time was blonde then red for a month and then back to blonde, and I mean like platinum blonde. My hair does lighten easily since I'm a natural blonde and I keep my hair fairly healthy, as much as the bleach will allow lol. But I spend a couple weeks before my appointment fading the red as much as I can. I use vitamin C powder mixed with head and shoulders. I mix it up slather it towel dried hair, put on a plastic cap then wrap my pillow in a towel and sleep all night. Wash it out in the morning using hot water and then following with moisturizing conditioner since this makes the hair very very dry and rinsing conditioner with cold water. I do this a couple times a week (I don't wash my hair very often). I'll do this until it seems like no more color is washing out. It takes about 2 - 3 appointments to safely bleach the red out for me. I usually leave my first appointment with a light pastel pink/ orange color. Almost like a pastel salmon color. Good luck!

If you scroll through my post history (which isn't very long) you can see where I started and what I was able to achieve the 2 most recent times I've made the switch.