Your companion
If you're a budget solo traveler in Mongolia, and you're looking for other passengers to join you on a trip during the given duration, be cautious about your companion. There are offers to split costs on a trip through rural Mongolia from time to time, but you should decline since you couldn't locate another group.
It's understandable that you want to save money, but some folks you don't know about your companion will sabotage your trip. They may be bone dry in personality, meticulous in many areas, and easily/unpredictably offended by a variety of things, ranging from seating arrangements to requesting bespoke diversions.
Their presence will make you understand how important it is to carefully select who you want to accompany you on the trips. You'll be deep in the rural desert, far from the capital, once you've joined the trip. There is no going back and no money back. When there are no other distractions but each other's presence, your travel companions may either dampen or elevate your attitude. Choose carefully if you are sensitive to the social energy surrounding you.