In some parts of the world 'biting' is synonymous with 'stinging'. Here we are using the term to describe a pincer like gripping action of the mandibles which may be either strong or weak according to the activity involved.
The action of biting occurs during wax work and comb building, but here we are concerned with the behavioural aspects of biting in relation to other bees, humans or other organisms. This activity does not occur in all strains of bee, but has been observed in 'Russian' stocks and some Amm stocks. I personally do not mark it down as a bad trait unless it occurs with 'head butting' and/or 'following'.
Some strains of bee will bite or attempt to bite human skin, most particularly the forearm. such biting varies in degree of persistence from being a minor sensation up to the drawing of blood. with three or four bees being actively engaged in this at any one time.
During balling... the queen's legs and other appendages may be damaged as a result of the bees biting the queen in a fashion that indicates hostility.
I am not sure if there is any direct genetic linkage, but other behaviours... Head butting, hair pulling and following are often associated with biting, however it is not always the same individual bees that exhibit the behaviour, but commonly bees from a particular hive will exhibit several or all of the behaviours.
During drone eviction, workers will bite leg joints and wing attachment points, such actions rarely sever the part concerned, but damage is severe enough to render the drone incapable of flight or the ability to climb up woodwork in order to re-gain entry to the hive.
In 1891 (give or take a year)... A British beekeeper named John Hewitt imported so called 'Punic' bees from Tunisia, he found and described thelytoky in these bees. These bees were reported as having been small, black, spiteful, and with the habit of biting humans in addition to stinging.
In Thelytokious bees... Worker bees can be seen biting each other, or particularly other worker bees with their abdomens in a cell in what could be described as an egg laying attitude.
Mite Damaging is mainly caused by biting. The larvae of wax moth (both species) are also harassed in this fashion.
Hair pulling is included here as it is often coupled with biting and can be exhibited by the same bee within seconds of having bitten or attempting to bite. The hair is gripped in the mandibles and the legs of the bee are braced against the skin to provide an upthrust to the body. I have never had a hair actually pulled out, but some bees can exert a pull that is uncomfortable if not on the verge of pain.
On a few occasions the pull is exerted in a vibrating fashion, the frequency of this vibration is similar to that which occurs in a worker that is attempting to sting something tough like a leather glove.