Soloing is not a waste of time. It's the best way to farm for specific pieces of loot in the late game, and best way to make money in the early game. Early on, companions are a total liability and they just gobble loot and renown.
For bandit spawns, there's a lot of luck involved. Especially at the beginning when you have low Spotting skill, there might be a bandit party nearby but you won't see it. But even then, usually on Day 1 there are 5-6 man bandit parties near where you start.
In terms of soloing, the priority is to get a couple of decent shields. With 9/16 stats, you can go up to 5 riding, WM, and shield very early which is a solid defense. Bandit parties usually don't give more than 1 renown per 2 bandits, but they drop a lot of aketons and other chest armors that sell for 150-250 each. If you clear 10 of them per fight, plus some other random crap, that's close to 3k denars at 3 trade.
Best sources of renown are soloing Heretic parties or Knights of the Dawn. Dawns have no missile weapons and Heretics have pretty lousy firepower. Beating a ~20 man Heretic party solo will net you about 40 renown. They don't provide as much loot, but the Heretics can drop good stuff--in my current game (day 29), I've already looted a rusty RBS and a Netherworld Charger. I think I had 200 renown by day 15 or so, mostly off the back of two Heretic fights, one worth 44 renown and the other worth 41. Incidentally I already have 17/18 enterprises up and about half the companions recruited.
The way to beat Heretic parties is to ride in circles until they waste all their throwing weapons, and then couch down the crossbowmen with the riders chasing you. Then couch down the remaining foot troops. Then, you ride in circles to your left and you slash the riders' horses in the face until you kill all the horses. Periodically couch down the dismounted riders if the AI is getting bogged down too much. The biggest threat will be Heretic Magni with RBSes, since if they land a good hit they will one-shot you.