It's not uncommon for the nominee to pick one of his defeated rivals. Sometimes this ticket wins (Kennedy-Johnson, Reagan-Bush, Obama-Biden) and sometimes it doesn't (Kerry-Edwards).
I can't see Bernie offering it to Hillary and I can't see her accepting it.
Nevertheless, the basic idea of trying to unite the party for the general election is a sound one. Whoever wins the nomination will need the votes and active support of as many of the other candidate's adherents as possible. A ticket like Sanders-Turner or Sanders-Gabbard would thrill the Bernie Sanders Group on DU but would leave millions of Clinton supporters feeling completely excluded.
By contrast, Sherrod Brown is a good liberal Senator, he endorsed Clinton, and he would help deliver Ohio. Possibilities among women would include Kirsten Gillibrand, a Senator who endorsed Clinton, and who, before being appointed to the Senate, showed an ability to win in a somewhat conservative House district. A downside is that she won by being somewhat conservative herself, nor does a ticket of two northeastern Senators represent much balance in other ways.
My overall prediction is that, if Bernie wins the nomination, he will NOT pick someone who thrills the Bernie Sanders Group. We'll have to settle for being thrilled that he won the nomination, which I certainly will be.
On the gender issue raised by the OP, I agree that there would be benefits to picking a woman, but there are many other factors to consider as well. I would much rather see Sanders-Brown than Sanders-Turner.