Bara is used when mankind is first created "male and female" (Bereshith 1:27), like all the rest of the animals (see Sforno there) during the general narrative about the world, predominantly in the first chapter. But it is only later, in the narrative specifically about the garden, where it refers to HaShem "forming" Adam (2:7).
If you read RambaN and Sforno there, they discuss the differences between the reference to bara versus yassar in these two passages, the latter meaning to merely alter an existing object, whereas the former usually infers an initial bring into existence (although Ibn `Ezra and Gersonides dispute this point, but that is not relevant right now).
During the sheva` berakhoth, we say "yosser adham" because while humanity was first created as essentially an animal creature like all others (Sforno), God later "formed" him into a different man - one that was sedentary, agrarian, domesticated animals, and - most of all - practiced marriage.
"Yotzer HaAdam" indicates the new state of man just before he is given his wife by God, like a man under the huppah.
Hope this helps.