The advice you have already been given, to try your plunger again, but this time blocking the basin waste and both overflows is good advice. You can also try blocking both overflows, filling the bath and basin with water, then whilst running water into your basin, take the bath plug out, and give the basin a vigorous plunging. You will probably make water go everywhere, so ideally a few handy towels for soaking up, should be at hand. Then as the bath is still a third full, try a vigorous bath plunging, with lots of upward force, you may see bits pulled up through the plug hole, try and catch them and pull them out by hand. If you do manage to clear the blockage, then in the future, if you normally & mainly use your bath to shower in, and do not have many actual baths, which lots of people do, myself included. It is a good idea, to occasionally fill the bath and then just empty it, this is because if it is used just to shower in, hair can easily build-up to a point where it forms a solid plug in the waste pipe, and the extra force of water when emptying a filled bath, can make all the difference in keeping the waste pipes clear. Good luck.