My superior is always asking me to go drink with him/her
My boss asks me out to drink quite often=結構頻繁に上司が飲みに行こうと誘って来る
ask someone out=誰かを(出掛けようと)誘う
「飲みに誘う」だと「ask someone out for a drink」
My superior is always asking me to go drink with him/her=上司がいつも飲みに行こうと誘って来る
上司の事は「boss」や「superior」と言います。
いつも断ってる=I always turn him/her down