The main playstyle for Ash that I've found is simple. You have to be hyper-aggressive and CC the fuck out of everyone. At the start you wanna take cauterize 1, and choose the second buy off the enemy comp. If they have lots of cc, grab resilience.. If they have a skye or sha-lin, grab iluminate. You get the picture there.
There are 2 ways to play Ash, depending on if you are a point or off tank. I'll start with the off tank guide, as that is the place where ash shines.
As an off tank, you can have 1 of 2 goals. You either want to boop everyone off point and keep an aggressive zone, or you want to bully someone that is going to give your team trouble. Start off by getting to point and dismounting just before you touch. Charge your burst, then dash in before the enemy can get on point. Try to boop as many of them bak as you can so your team has time to get free cap progress. Once you have them booped away, toss your shield down to stop them from farming free damage as they walk up. At this point you can either try to keep them off point with your CC, or you can chase down a healer or dps to keep their focus off of damaging/healing the players on point.
As a point tank, the strat is relatively the same, however there are some key differences. You don't want to dash off of point to bully someone, as there isn't anyone to contest point if you are gone. You want to save your dash as an escape. Use your shield as if it was a barik shield. It moves slow enough with the talent that it basically acts as a stationary shield. Use your boop to keep everyone off of point, and focus damage on the tanks. If they have a luna on point or a barik with turrets, I would focus those over the tanks. Let your DPS do their thing, and just try to keep everyone off point. Your kinetic burst has such a short CD that if you hit a good boop, by the time the player hit is back within range, burst is up again.
Some general playstyle tips:
If the enemy has a viv, shoot just above or below her, the splash damage from your shot will go around her shield.
If there is an airborne threat (andro, drog, willo in ult, etc) drop your shield and dance in it. Go from one side to the other of it. This will make you a much harder target to hit, especially for willo and drog as they have to lead their shots, and it will lead right into your shield if you do it right.
If you are playing as off tank and are about to dash into the backline, always charge your boop before you dash. This way, once you are in the backline, you don't have to spend precious seconds charging, it's already good to go. You can easily catch a healer off guard with this nd boop them right off the map.
As an off tank, use your ult to stop enemies from pushing point. Use it when you have a good zone, and drop it in a choke point. The stun is nice, but the main power comes from the damage immunity. Use your ult to buy time so your team can get free cap.
As a point tank, there are 2 ways you should use your ult. If you are pushing the payload, ult a little bit ahead of it, so that as the payload pushes it comes in to your immunity zone. Keep the enemy pushed back and get some free progress. The other way is as a last resort to confirm an overtime touch. If you are low and have to withdraw from point, but you are about to lose the OT, consider ulting on point to buy some free time for your team to come back and help you out.
The build is focused on keeping everyone off of point, or alternatively, bullying someone all the way back to spawn. We want to use kinetic burst as opposed to the dash for 2 reasons. The first reason is that the dash is easily stopped by any CC (khan grab, damba stun, etc). The second is that it's simply easier to hit. This build is great because you can use it as a point or off tank. As a point tank, you want to take Fortress Breaker to shield your team. As an off tank, you want to take Battering Ram so that you can easily dash in without worrying about getting chunked.
Increase the Knockback distance of Kinetic Burst by 8%.
Reduce your damage taken by 24% for 2s after using Shoulder Bash.
Increase the Knockback distance of Shoulder Bash by 8%.
Reduce the Cooldown of Kinetic Burst by 3s.
Heal for 120 over 2s for each enemy hit by Kinetic Burst.