I've seen Ashley Lawerence a handful of times and she charges a bit extra to record video of the session. I didn't think I'd enjoy it but I've come around on it. Are there any other GSE/PSE providers that offer this as well?
It's pretty rare for providers to advertise they allow recording. You're going to have to build an relationship of trust with a provider before you can ask if it's something they allow.
You can understand how privacy and discretion can be an issue.