Making salted caramel popcorn - how can I remove the bitter flavour?

Baking soda does indeed have a very bitter flavor, it can be a good addition to sweet foods like caramel corn but can be unpleasant.

Its purpose is usually to lighten and soften the caramel, it is essentially a leavening agent since it reacts with the acids in the caramel to create tiny bubbles. So if you omitted it, the caramel would be less light and soft. You could try to offset this by adding something like butter, but this would quickly get into the complex chemistry experiment that is caramel, it is very hard to get the right texture and it can become too sticky, or too hard, or too soft, etc.

I've watched the video that you mentioned and being a pastry chef I can guarantee you that the bitterness is not due to the bicarbonate of soda even if in the video he uses a huge amount of it. The thing that is causing the bitter flavour is actually the method that he uses to make the caramel itself. Dry caramel is one of the most difficult ways to make caramel because it tends to burn really easily - in fact, it is normally made by adding sugar a bit a time, not all at once, this way you can avoid the burning of the sugar at the bottom and on the side of the pan (as you can clearly see in the video that you linked the side bits are already super brown and boiling while the sugar in the center is still solid).

So my advice to make your life easier will be to put the sugar that you need in the pot and add a bit of water, just enough to moisten the sugar a bit, put in on the heat and let it caramelise without stirring, it will take a bit longer but you can control the colour better, when you reach the colour that you like (it should be a slightly dark amber color) stir in the salt and the butter, turn off the heat and add the baking soda.