Humidity is your biggest enemy when it comes to dust mites, so the first thing would be to ask directly if the hotel can keep the room at a low humidity level (ideally below 50%). If they have climate control, even better. It's also worth asking whether they'll let you bring a dehumidifier or a portable air purifier, because some hotels don't mind and others do.
Apart from what's already mentioned about high-temperature washing, I'd ask if they actually use waterproof covers on both pillows and mattresses (not just the mattress). And if possible, ask them to change the bedding on the day you arrive, not just have it ready. Some hotels will do it without any problem. You can also ask if they have rooms with fewer textiles - fewer curtains, fewer carpets - because that cuts down on places where the bugs can nest.
One practical thing: bring your own dust mite covers from home and ask them to put them on the bed before you arrive. That way you know exactly what's underneath you. And if you've got the budget for it, look for chains that explicitly advertise hypoallergenic rooms; it's not a guarantee of anything, but at least they're already thinking about it.