Pick Out the Best Traders
The wasteland is full of traders, whether they have set up shop in a city or a diner, or constantly travel the world with their Brahmin caravans, there are plenty of opportunities to trade. On your travels, you’ll come across some traders who have a lot more ammo to sell than others. Trudy, for example, at the Drumlin Diner just to the west of the Starlight Drive-In, is one of the best vendors to grab ammo early on in the game.
Make sure you keep a note of the vendors you stumble upon who have a ton of ammo so you can revisit them in the future. It’ll save you from wandering around the vendors of Diamond City, who tend to lack substantial quantities of ammo.
Oh also, check the inhabitants at your settlements. A lot of them are carrying items that you can take for free, and a load of them have a good few bullets worth pinching before you head off on your next quest.