To all golf people out there....!!?

Okay so i'm just wondering about my bag. Is it necessary to have a cover for the bag? Because i've noticed at the golf course that many don't have it. And i lost my putter AND hybrid cover. XP I take golf lessons with my coach. I don't want him to get pissed because i don't have a cover for my putter. I took the cover off my bag but you can see my coverless putter and hybrid. So what shall i do? I have golf class today and i feel a bit embarrased because i don't have covers. Thanks.