The following sources of arrows are available in old school RuneScape. Cash, skills, and combat levels determine which methods are best.
Arrows can be purchased from Lowe's arrow shop just south of the east varrock bank. Brian sells arrows in Rimmington, but only has steel through adamant. Arrows and arrow tips can be purchased in Catherby just east of the bank. Sometimes, arrows are found in the general store when other players sell.
Arrows can be fletched, if the old school RuneScape player has the right fletching and smithing level. Smithing is not required as the arrow tips can be purchased from other players and from the shops. Use a knife with normal logs to make arrow shafts, and then add feathers. Lastly, add the arrow heads.
Arrows of all levels are also obtained as a monster drop from various NPCs and can be thus obtained. Arrows can also be picked up from spawn locations and from drops by other old school players who don't pick up their ammunition.
Bolts can be obtained in similar ways as arrows, and some shops stock bronze and other bolts. They can also be smithed or obtained from other players.