No, it won't get bitter, but it will flower and not produce any more leaves. It will go on for a bit longer but then you have a gap before spring sown chard is ready to harvest. You can harvest and freeze now. Chard freezes fine, I freeze the stalks and leaves separately. The leaves just get chopped and put in a freezer bag. The stalks cut and blanched for one minute in boiling water, then taken out and put into very cold water to cool them down fast, then frozen.