I would use a mix, but it would include the bow in a secondary role. Assuming easy access to ammo, I primarily would use a rifle or perhaps a shotgun. Numerous traps would also be needed.
If the apocalypse had happened, causing a physical security risk, the bow would play a much more prominent role. Game laws, conservation, and ethical hunting practices would go out the window in a true live or starve situation.
I have read a lot of stories about people who went on bow based survival hunting trips. This would be fun, but I sure hope it never happens to me for real.