I would strongly suggest widening the champ pool a little bit. Ashe and Varus are great adcs, but are often immobile. They have great engage potential, but if caught out, they have no escape ability aside from using your ults.
I would suggest Jinx, Caitlin, and Lucian and Tristana to add and practice. I would also try to make sure you're build path is accurate and make sure what your building complements your carry.
Look at the enemy team in champ select. Obviously if you're first pick you're kind of in the blind, but you can offer to trade with people so not to get countered. With that being said, if you fall mid select look at their team comp and then based on it, try to gauge which ADC champ would best fit against that. You don't want to have a ADC that has low mobility if you're going up against heavy engage potential. You want to aim for a champ that has an effective out method. Trist, Jinx, and Lucian offer some of that, Caitlin as well.
If their team has a lot of CC you want to look into a Guardian Angel an a QSS/Mercucial so you can get out of it.
Don't blame teammates, you're all on the same team, and you could be making mistakes without knowing you are.
Map awareness is crucial, wards are key. Everyone should be warding, trinkets and control wards help.
One last thing is positioning and targeting. Your position defensively will keep you alive, and your positioning offensively will help you carry. You should not be front line in a team fight, and you should always be auto attacking even if your abilities are on cool down. Don't attack the tanks, if you don't have too. Aim for their carries while they are attacking your tanks. Even if you die, but your teammates get kills, that helps swing the game in your favor.
One last thing, don't chase for a kill. Try to recognize when it's bait. If you get someone super low, don't flash under turret to get the kill. Just be patient, if you were able to get them that low, you'll be able to do it again. People often think Kills are what win games, but that is not the case.
Hope this helps.