Worth noting that during the Petersburg siege the A of N VA paid for scavenged bullets. A of the Potomac skirmishes & pickets were ordered to fire 100 rounds during their shift. The intent was constant pressure & harassment, not sniping. This policy resulted in rich pickings for the A of N VA recyclers.
As a volunteer at Stones River NB I got to go places no visitor sees. In the storage area of the museum there are five gallon buckets of found bullets. The maintenance people add to the collection regularly. During the metal detector survey of the site of a munition train behind the firing line on Dec 31, 1862 over 300 dropped bullets were found.
On family land north of Nashville the area around a big spring was a camping & skirmishing spot for Indians, long hunters & Civil War soldiers. Uncle Sam kept a sack hanging on the plow. As a teenager I couldn't lift the paint buckets of bullets he had.
The point being buyer beware. Anybody can mold & shoot lead bullets using an original mold. Antiquing the resulting relics is a simple process. A host of folks here on CW Talk can attest to the large number of shot impacted bogus belt plates that they have encountered.
There is no shortage of Civil War bullets. More are collected every day of the week. Collecting relics is a great hobby, of that there is no doubt. However, be aware that there are people who make their living making & peddling fakes.