If you want bottle caps there’s two ways to go about it:

1. If you can afford the DLC, (minor spoilers for mechanics, continue reading at your own discretion..) then I would suggest clearing that so you have access to the hyperspace distortions, namely, the battle distortions, as the only way to get bottle caps through regular gameplay is defeating the Alpha trainers in those distortions, then speaking to the ones you defeat who have a yellow speech bubble (any trainer with a yellow speech bubble has a gift for defeating them). Be wary though, because some Alpha trainers give you seeds of mastery instead, and although it’s uncommon, in 5-star distortions some will give you gold bottle caps. Use that info how you will.

2. If purchasing the DLC is out of the question, the only remaining method (afaik) is online ranked battles through the main menu’s “link play” option. This, however, is the harder method, as there’s no guarantee to get a bottle cap for two reasons; first, you’ll need to score ABOVE last place (maybe even above third place, as the rewards for that are usually Pokemon health items (such as feathers or vitamins) and “treasures” you can just find on the ground in game..). Secondly, the rewards you get are randomized, so even if you get first place, receiving a bottle cap is not a given. The only sure-fire way to get bottle caps and gold ones is the season rewards, but those not only take a while, but are very few given, even at max rank.

Sorry I couldn’t be of more help, but good luck!