Basically you need to first decide how you want to do this using the QuickBooks User Interface first.  You can enter the charges directly into each customer's register. You can also transfer reimbursable expenses to a billing statement.

Open the appropriate customer register and cChoose one of the following two options:

• Click Customer Center. Select the customer or job that the statement charges apply to. Click New Transactions at the top of the list and click Statement Charges.
• Go to the Customers menu and click Enter Statement Charges. Verify the name shown in the Customer:Job field. If the charges are for a different customer or job, select the correct customer or job from the list.

(Optional) Change the date of the statement charge.

In the Item field, enter the item you use to track this kind of charge.

Enter the quantity in the Qty field.

(Optional) Edit the description that QuickBooks provided in the Description field.

If you have more than one A/R account, click the account that you want to use from the Account drop-down list.

(Optional) Assign a class to the sale.

Click Record to record the charge.

If you have other charges to enter:

• If the charges apply to the current customer or job, continue to enter them in the register below the charge you just entered.
• If the charges apply to a different customer or job, choose that customer or job from the Customer:Job drop-down list at the top of the register and enter the charges.

When you're ready, you can create the billing statement.

You can use the A/R register instead
You can enter all your statement charges directly into your accounts receivable register instead of the individual customer registers. If you have a few customers, or if you like to see all your statement charges listed in one place, you may prefer the A/R register. Of course, each charge you enter in the A/R register also appears in the appropriate customer register.

After deciding how you want to handle it, enter a test statement change and examine it's entry in the Charge and ChargeLinkedTxn tables using QODBC.

See: Statement Charge Insert statement fails for more