I was trying to create a new non inventory item under the Billable Expenses account. However, I could not find the said account from the options.
Non-inventory items are not transactions. They are shortcuts used when entering transactions. You cannot create a non-inventory item under any account. You can only create them under Settings. See the Guide:
https://forum.manager.io/t/non-inventory-items/7344
If you are referring to trying to pre-assign a non-inventory item to the Billable expenses account, that cannot be done. The reason is that non-inventory items cannot be assigned to control accounts made up of subaccounts. That includes not only Billable expenses but Billable time, Accounts receivable, and so forth. Without knowing a customer in advance, for example, Manager cannot make an assignment to Billable expenses because the transaction would be incomplete and end up in Suspense.
Furthermore, non-inventory items are for things you are buying or selling. Billable expenses are purchases made on behalf of a customer that will be reimbursed.
What kind of thing are you trying to record? Maybe there is a way to accomplish what you want to do.