Is this B2C or B2B? Large companies or small companies? Small or large payments? Recurrent billing of fixed amounts or variable amounts?
With large companies or companies which do a lot of business in USD you might possibly get away with a USD invoice. (Larger companies will typically have USD accounts as well as CAD accounts).
Otherwise a CAD invoice / payment by CAD cheque OR accept credit cards (for smaller amounts).
As a customer, it costs me/my business too much effort/money to draw a USD check on a CAD chequing account.
The best solution depends upon the nature of your business and the costs involved.
As long as the Canadian check is MICR encoded and payable in US dollars, it will be accepted in the US. If either item is missing, you will pay a fee to clear the check.
Note that billing customers in Canada from the US by mail can add up to 20 days of delay to your receipt of payment (up to 10 days for them to receive the bill and up to 10 days for you to receive their payment.)
You might want to bill them via email, and taking credit cards will make it easier for your customers to pay and faster for you to receive payment.