I never really found the veil to be distracting. I find I am more in tune when I wear it, and even like to do so when praying the rosary at home.
I started wearing mine in Lent. I was in the choir and a cantor at the time, and wore a black chapel cap when I was cantoring. I offer my veiling for offenses against the Holy Sacrament becuase of immodest dress. I find this helps me focus, as long as I am not watching the communion processions, LOL!