Sure it asks you to be patient. It also warns against doing anything aggressive in an attempt to change the situation for the better. It asks of you to neither give up, nor act out of desperation. Just stick with it as best you can as is until further notice or things work themselves out. I agree, It does suggest thing will change for the better eventually.

It means wait for the bad things in your life or a situation to pass, and hope they get better

This phrase can be simplified when you compare it to the word 'patient'. When someone says to 'bide your time', they are meaning that you wait, but its more of a proactive wait. In the context of this phrase, 'hold out hope', means to hold onto your hope for the thing you are biding your time (or waiting) for. So, no matter how long you wait, don't let yourself become discouraged and lose hope.