Silver used in the supernatural sense probably derived from its power of killing bacteria and will turn black(oxidize) when in contact with certain types of poison.
Even if you are used to making your own bullets, makeing silver bullets is hard. Silver melts at 962C (1763F), while Lead melts at 327C (621F). This means that lead can be melted in a crucible over many commonly available heat sources (gas flame, wood or charcoal fire), where silver requires facilities not commonly available.
Additionally, Silver has smaller thermal expansion than does Lead, which means Silver bullets cast from the same size mold as Lead ones will cool to a slightly larger size
And Silver is harder than Lead, which causes problems sealing against the gunbarrel during firing, taking a stabalizing spin from barrel rifling, and transfering energy to the target.
The only reason to use Silver bullets is because of its purported supernatural properties, i.i., as a bane round.
Never tell people how to do things. Tell them what to do and they will surprise you with their ingenuity. — George S. Patton
"It would also be rather ineffective in real life in most modern firearms, as a bullet made entirely of silver would be too hard and light to properly take advantage of rifling"
According to Wikipedia[1], silver falls between lead and copper in hardness. Given that both of the latter are common bullet materials, silver's hardness would not make it unable to accept rifling.
Edited by Korbl