I think tails are a recessive trait when it comes to half-saiyans. (still not sure about quarter saiyans like Pan, but it could possibly be the same situation with them as well) Bulla was obviously not born with a tail, as the viewers saw her birth. In following episodes after her birth in Super, she is never seen with a tail. Trunks didn't have a tail in DBZ when he was a baby either, and same with Goten too. Gohan must've gotten lucky with his tail, as he's the only half-saiyan on Earth with a tail. We know as a fact that pure-blooded saiyans (from Universe 7 that is) are always born with tails, so that biology must get a bit messed up when a saiyan has a child with a human. Also, I'm pretty sure that the lesser amount of saiyan blood that someone has in their body, the least likely they are to have a tail. Goku Jr. and Vegeta Jr. were not seen with a tail, and they are 1/16 saiyan. Pan was not seen with a tail either, and she's 1/4 saiyan. It must be more common with half saiyans, but of course, since tails are a recessive trait, that doesn't mean all half-saiyans will have tails. That's really all I can think of, I don't see any other reason why Trunks, Goten, and the others don't have a tail.
I already explained that just simple recessive inheritance wouldn't work here, because all of the half-Saiyan children have the same genotype, so either all of them have tails or don't. If we take the tail locus as "T-t", where "T" means they have no tail and "t" means they have a tail. Goku and Vegeta would have the genotype "tt" since he had a tail, while Chi-Chi and Bulma have "TT" for no tail. All of the first generation half-Saiyan children would have "Tt" since they are halfbreeds.
The recessive thing only works if two hybrid parents (both "Tt") have children. So that 1 in 4 of their children would possess the "tt" genotype.