Good day, enquiries-bnd.
A bill is automatically added under the Project Costs as long as it's using an expense-type of category. You can open the bill and double-check the category used under the Category details section.
If an item or service was used in the bill, make sure that it's using an expense-type category in the Expense Account field when it was set up. You can go to the Products and Services window to double-check if they're mapped to the correct expense accounts.
After making the necessary corrections, go back to the project you're working and check if the bills are already listed under Costs.
You can also visit this guide for more insights about tracking project costs and income in QBO: Track Income, Costs, And Profitability By Project.
I'll be around if you need more help when adding transactions under Projects.