Hi info-armi-la,
Welcome to Community! QuickBooks Online is a powerful program with the features you need to import your data seamlessly. However, there currently isn't an option to include classes, when importing bills.
If you would like to see this available in future updates, please don't hesitate to submit a suggestion to our Development Team. Customer recommendations are greatly appreciated in helping to improve your overall customer experience, with QuickBooks Online.
Please feel free to reach back out with other questions. We'd be happy to help!