Im not familiar with UVA business school too much but I know at Emory and Wake Forest they have to get admitted to the B school after youre already in. In these and I assume UVA also, you go in with whatever major, usually economics or something of the like at the school and take the required pre business courses like accounting and all that. They obviously don’t take everyone so its a bit of a gamble but if youre willing to work hard to earn a high gpa at UVA, it might really pay off to get into the business school later on.
As for other good B schools in Virginia, U Richmond, Washington and Lee (not a B school persay just the major but its a really good one!), VTech, and supposedly William and Mary although I don’t know too much about that school.