Direct Express doesn't make routing or account numbers publicly available for their cards.
No payments (except returns for purchases made with the card or PayPerks prizes) can be added to the card—it's only for the funds you receive for your federal benefits payments.
If you're trying to set up online bill pay, look at the company's website and see what information they need.
You can pay bills online with your Direct Express card as long as the company processes them like a credit card transaction (asks for your card number, expiration date, etc.). If the company asks for information like a routing number, you won't be able to do that with your Direct Express card.