I just have to say Thresh doesn't have any self heals and early levels he has zero tanky stats.
I main support so i deal with thresh. They do try and act cute with me all the time. Unless my ADC plays stupid and gets caught i will punish thresh harder then he can punish me.
Only supports i consider strong. Zyra, Sona, and Taric. All other supports i have played are weak
Thresh - Has no sustain or natural defense. Play champions with heavy pokes and disengage. Zyra, Karma, Janna, and Taric. I would say Lulu, but she isn't worth it anymore.
Zyra or karma: just throw crap at thresh or the adc and profit.
Taric: just stand between thresh and your adc. Treat him like blitz and if he gets close stun him and hope your adc follow with a few attacks then back off and if he hooks you stun his adc and go ham.
Janna: More of a safe pick for disengage.
Lulu: The old way was CC ADC and kill him when thresh hooks your adc, but early levels her mana cost is really bad. So you might be oom when its needed, because unless your adc knows how to play with lulu she will make you blow your mana trying to save her from just harass
Edit:
I see you're a ADC "Ashe" Main. I hate to tell you ADC will have no control over bot lane. It really only comes down to supports and second you play ashe no mobility so thresh will catch you eventually and if they get away it is because you have no mobility. Most likely you use your ult to initiate or they just dash or flash out of the way.
Once again bot lane is all about the supports. if you are losing to thresh its because of your support.