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Gacha is always a gamble. You can't be "screwed" because that's what you sign on for in gambling. It sure does sting, and it would be great if drop rates were posted/improved but as long as people keep throwing money at the current model, they don't have to.
The bag has a 1/10,000 drop rate. Why 1/10,000? 1/1,000 is too common and 1/100,000 is too uncommon. Even if you open 10,000 boxes you have a 64% chance of obtaining the bag. Therefore if you completely fish up 100% boxes with all of the 3150 bait you're given, you have a 28% chance to get the bag. I could be wrong about 1/10,000 but, it has to be between 1/1,000 and 1/10,000 but the latter seems more reasonable for DevCat standards.