Bored: Between the tire and the tank you're really getting some post-it mileage here !
Lesseee.... There are a number of options. The first would be to do a fast, fix-it and continue to ride.
If, for example it were a nail found in the tire then a small can of fix-a-flat can (potentially) get you out of having to wrench at all. ....but you gotta carry the stuff.
Alternatively you can plan to dismount the wheel and tire from the rim and patch, or lay a new tube in. ....which means of course you have to carry all that jazz including a pump, or CO2 inflater too.
When you have large rocks and/or tree stumps around that makes the latter plan easy. If not yea, you either lie the bike down and do it that way, or get what is referred to as a swing stand (a side stand that when working with the OEM stand, actually holds the rear and up in the air).
There will be times, of course following Murphy's law, that you will be in the worst place ever to have a flat. ...and that, unfortunately, is what you have to plan for.
P.S. if you are going to make a choice to ride alone out in the bush somewhere, don't forget to either tell someone, or leave a note where you are going.