I am ashe opponent is katrina. We are playing 3v3 and both solo top. Ashe has slow movespeed, and kat has blink strike / insane burst.

How do I not feed?
Harass Early: Did that, ended up getting a kill, but after that I felt helpless
Use abilities to avoid death: Tried that, I had flash and ghost, and it was not enough.
Tower Hug: Tried that, ended up coming being under leveled and got tower dived insta killed.
Call for backup: My ally's had there hands full
Lane Switch: This worked wonders, singe was a better match-up it seems.

But after trading with Kat 1-1, she ended up "Carrying" the entire match and team wiping us all day.

Some tips for this matchup? Be much appreciated!

maybe arrow her when she dives other than that dont play ashe in 3s..... and certainly dont go top

I don't play much threes but in SR I play a lot of mid so see quite a bit of Kat. Wait until after she use Shunpo to engage. Wouldn't ever suggest a 1v1 with Kat. Particularly not with Ashe.

If you are playing 3v3 I wouldnt use an ADC.
Definitely wouldn't pick ashe.

Ashe's early game is fair at best, and 3v3 is so snowbally you need strong early game champions.