A heat bath is another name for a heat reservoir. It is not part of the system undergoing the process.
It has the property of remaining at constant temperature, however much heat it accepts or provides.
However the system may or may not remain at constant temperature. Heat is transferred from/to the heat bath by the system process. If pressure remains constant no work is done so all the heat transferred increases/decreases the internal energy of the system.
As an example, you melt some ice at constant pressure by adding latent heat from the surroundings (heat bath).