Re bill payments. On line banking. Works great even when you are home.
Re mail. If possible, have someone collect it at your house every couple of days. Then every 2 to 3 weeks they can forward it to you via UPS or USPS. Many campgrounds will accept mail and if you plan ahead you can have it sent to a campground you are planning on being at the next week.
We also have it shipped via USPS to General Delivery to a small town we are traveling through. Need about 2 weeks lead time for this method.
Enjoy your trip.