If you are looking for the (single) antagonist of the story Lyddie, I think you have to go with Lyddie herself. The bank, the bear, Mr. Mardsen are all good choices for antagonists. They are antagonists. But the main antagonist I still think is Lyddie. Or at least her attitude regarding money.
Gaining financial independence is all consuming to Lyddie. She is farmed out to work at the tavern in order to help pay off family debts, but she feels equivalent to a slave. Working at the textile mills offers her a chance to make more money and make it faster. That way she can pay off the debt and no longer be financially in debt to anybody. Lyddie also wants to be financially independent enough to not have to depend on anybody except herself.
This single minded focus of hers is admirable, but it ultimately hurts those around her. For example, at one point in the story Lyddie is asked to teach a new Irish worker how to work the looms. Lyddie is so frustrated by the end of the day at how much her own work is being slowed that she tells the boss to give the new worker her own machine. That would be okay if Lyddie was confident that the new worker could work the machine, but Lyddie knew full well that the worker wasn't ready and was likely to get hurt. Lyddie's focus on herself and her ability to earn money put someone else at risk. It's not until the end of the story that Lyddie changes her main focus and decides that the best way to improve herself is by getting an education.