At some point during every stalk you need to transition from hunter to shooter. Getting close to the animal without spooking it is the first step. But it's your skill at arms that will determine whether you notch your tag that day.
Only under the most unusual, and favorable, circumstances should you consider taking a shot from an unsupported, meaning off-hand, position.
Anything that helps to steady your sights on the animal's vitals is a candidate for a shooting rest. A quick glance around the environment generally reveals a bounty of potential supports. Even grabbing a handful of sagebrush or juniper and laying your rifle across it can make a huge difference.
And, of course, there's the gear you carry with you. Even if you don't have a bipod or shooting sticks handy, a jacket, pack or binocular can all create a steady platform for your rifle.
Lastly, don't be afraid to give up some yardage to make a better shot. Backtracking 25 yards to a tree or rock that affords a better shooting position can be a smart tradeoff.