Can bacterial conjunctivitis be spread if there's no discharge or redness in the eye?

With no discharge or redness, it is unlikely conjunctivitis is present. With or without such symptoms, bacterial conjunctivitis is not transmitted from one person to another.

First off, bacterial conjunctivitis in healthy adults (who do not use contacts) is rare. Usually, the culprit is something else. I suggest getting an exam from an ophthalmologist.