Breathing out of the BC bag used to be something that was discussed and considered much more commonly than it is today. That was in the days of J-valves, no SPG's, no octos, etc.
Many people recommended periodically rinsing the inside of the bag with an antiseptic agent to kill any potential bugs in there that could lead to a lung infection later.
Someone recommended having to estimate how much air to breathe so that you did not become too negative. That is not an issue, as you inhale from the bag into your lungs and the volume is constant. You can also exhale back into the bag as your expired air still has about 16% O2. It also contains CO2 as well, but for a short ascent to the surface CO2 buildup in the air in the BC is not as large a problem as it would be simply doing an ESA. And on the way up as you need to vent air, just exhale it into the water to avoid putting more CO2 back into the bag.
It was never intended to be anything other than an emergency procedure but it did work and would allow an esa from a much greater depth than possible on a single lung full of air (or in some cases less than a lung full of air if there is not enough air in the tank for a last full breath - pretty common with high performance regulators).
It is not practiced or discussed any more as regulators tend to be more reliable and SPG and octo use is the norm, largely negating the potential to find yourself in a situation where the only air you have is in the BC.