You need to read the appropriate VA statute:
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+18.2-308
In the section titled "Except as provided in subsection J1, this section shall not apply to:"
"3. Any regularly enrolled member of a target shooting organization who is at, or going to or from, an established shooting range, provided that the weapons are unloaded and securely wrapped while being transported;"
So yeah, you're protected under VA state law. Given that you said you'd be putting them into a backpack, I would guess you're not going to have a rifle case on the back of your bike, so we don't have to split hairs about this statute being only applicable (or not) to the transportation of handguns. The law makes no reference in this section to a vehicle or not, so car, bike, or walking, you're all good to go. After all, if not, how could you walk from your car to the range with a gun in a case without a permit, right? Of course, you could just open carry...