Ur a smart player, you know when you should not c-bet so I wont patronise.
However I think an important part of cbetting is the amount. I dont know how mch you c-bet currently but I think 50-70% is more than enough. usually I go for jus barely above half. I used to 2/3-3/4 all the time but I have been convinced otherwise.
Also position is vital in determining whether or not to cbet. If I were in position and I had a hand that was not too strong, even like TPTK, I probably check behind. However, obv Im betting out with it if im OOP
To actually answer the question tho

yeah you should pretty much give up after one bullet early against an unknown. You need reads or a very good reason to fire another bullet IMO. Cbetting is less imp early in sngs