If you will be ordering the bags in bulk, then, China is a good place to get them made. Will save you a lot of money. Quality has improved a lot in cast few years. For material selection, design, and other details, you will have to connect with a designer. I can help with the research work and also shortlist manufacturers that can deliver a good deal. Email me at email@example.com to discussion more.
As you are developing the gym bag, I assume you already have the expertise on the material selection, design elements, quality expectation.
For manufacturer selection, 3 things are important.
1- Quality. How do they control their quality in mass production? What is their general approach? To save the day or continuously improvement?
2- Pricing as usual.
3- If they are really know what they are doing? Are they only manufacturing products or also designing/developing? For how long are they doing the business and how capable are they? This will help you to speed up your project, they can help you to solve the problems from the beginning. In design stage, prototype, manufacturing. They will also help with material selection as they have long time experience.
Let me know if you have any further questions. I am happy to help.
It all depends on the quanitiy.
If you are looking for a small quantity, with flexibility in the required design, you can literally search "gym bag OEM" on Alibaba.com
If you are looking to pentrate the market with a preimem bag, then your best bid is to connect with a manufacturer in Indonesia, where a lot of renownded brands work to produce their sportswear.