It is not known whether or not any of your stats affect the likelihood of having a successful trip. Traveling to a particular city several times increases your chances of success.
It is recommended to bring a gun and ammo, obtainable at the pawn shop, as well as 1 to 50 grams of cocaine. What you are carrying in your inventory can directly effect what happens in the city. While you aren't actually allowed to explore the cities you travel to, a number of events can happen while you're there. There are six cities to travel to, costing between $100 and $130 per trip, depending on the city. Traveling to another city is also an all day event, so it will be the only thing done that day. The buses leave first thing in the morning, so owning the alarm clock from the Pawn Shop as well as having caffeine pills the day before leaving is required. The Bus Depot is a Building in Stick RPG Complete where you can sell commodities, specifically Cocaine and bottles of beer, by traveling to other cities.