Samovar Tea: Let it brew the whole day?
The problem with black tea is that after a few minutes of brewing, the leaves release very bitter substances. There are 2 general ways to deal with this:


Short brewing time: remove the tea leaves or bag after about 3 - 4 minutes.
Saturation: if the tea water is saturated with non-bitter substances at 3 minutes of brewing time, it cannot take up much of the bitter stuff. Traditional turkish tea is brewed like that as well, so I suppose it should also work in a samovar.


The concentrated tea is an integral part of the system. You should not add any water to the svarka pot after initially brewing the tea or you give the bitter substances a chance to solve into the tea. 

The tea brand is important, too. I'd propose to try an Earl Grey or another tea with a light taste. Ask a tea shop for advice, if you have one nearby.

The ratio of 1:10 sound about right. Most people have to get used to the idea that barely covering the bottom of the cup is enough.

Putting the diluted tea into the big kettle is a very bad idea and probably won't solve your problem. Every green and black tea will get more bitter over time, no matter how it was brewed. I think keeping the concentrate for a whole day is simply too long. 3 - 4 hours is the longest I would keep brewed black tea. You could make smaller portions to use up the concentrate in time.

Experiment with different brands and different amounts of tea, always keeping in mind that you're making a concentrate to keep the bitterness out of the tea. A splash of milk can neutralize a little of the bitterness, but the milk has to be very cold for it to work. If all else fails, brew peppermint tea instead ;)