My suggestion would be to not try out-healing a DPS 1-on-1, at least not while they’re in range. Get away first, and once you’re comfortably far, heal up.
What I usually do, is trinket out, leg sweep and roll, trying to gain distance. I’ll use cocoon and ring of peace too if need be. Once comfortably far, soothing + enveloping mist, then either vivify, or roll/tiger’s lust and soothing + vivify, depending on how close they are.
The goal is to have as few casts as possible, so enveloping and vivify will almost always be cast during soothing. There’s still a short window where they can interrupt, but they have to close in on the distance first.
Having a statue down will also give you some healing, and you can insta-HoT yourself while running away. You can also use fortifying brew, and if specced into it, healing elixir (that one saved me in BGs quite a lot!).
There are a few azerite traits that help too, exit strategy and resounding protection being two of them.
In short, use your mobility to your advantage, and run towards your teammates instead of trying to fight them. Coccoon, Ring, Healing Elixir, Leg sweep, Roll, Brews and Teas are all super useful. You can thunder-tea + renewing mist to get some haste for a faster vivify - that’s sometimes more appropriate than soothing + vivify.
You can also drop a port while on the run, and port back (and run the other way) if they’re catching up. That usually gains you a few seconds while they figure out where you disappeared to. 