NY expressed precisely :
I can see that even if it's not the cause of the gurgling and back flow into
the bath, it's not a good idea to have water standing in the pipe because it
will (and does!) freeze in cold weather: several times I've had to dismantle
the pipework and pour boiling water down the section that is normally
horizontal/uphill, to encourage the plug of ice to emerge.

I would look to modifying that, it does need to have a constant fall,
to avoid problems of freezing and blockage from dirt. It is also bound
to cause the gurgling and slow drainage.