Well, it really depends on what type of bush flying you want to do. You certainly don't need to have thousands of hours to get your start, but that's what you'll be working to before a company lets you loose in command of larger aircraft. Face-to-face conversations are normally how you get these jobs, so it often means going on a road (or flying) trip to bug the Chief Pilot for the possibility of working the ramp. Knowing someone in the company or in the area often helps, but it's not how everyone gets their start. I knew a guy who got his first job by doing nothing more than helping one of the Captains with his bags when he walked up unannounced. It showed initiative, and the CP liked that.
There are opportunities in Africa, Northern Canada, and Australia - with the BIG proviso that you'll need the right to work in any location, so do your homework on these locations before you drop any money to fly over.
I started in "the bush" in Northern Canada with little more than 400 hours total time. Many guys and gals at that operator were starting with 250 hours. All of us sat in the right seat, and many left before cutting their teeth in the left seat. Consider that you'll be looking at having at least 3,000 to 4,000 hours before the average company will slide you across to the left seat, and even then you'll likely be doing a longer line indoctrination to make sure you're doing it right. All the good bush pilot Captains I know have north of 8,000 hours, mostly on the same aircraft type.
Plan on spending the first 5 to 10 years of a bush career with the same company. By that time you'll likely have the experience to move on to other companies as an experienced pilot.
Also - NEVER fly for free, unless you're swamping (a ramp agent flying with the cargo and NOT for the purpose of acting as a First Officer). If you agree to fly for free, the company will take advantage of you every step of the way. First it will be a reduced wage as an FO, next it will be top scale FO pay for your first year as a Captain. It will keep going for as long as you're with that company. I get things are different over in Europe, but they're that way because people agree to fly for free (or far too cheaply) and are relatively unwilling to take a stand to improve conditions. If everyone took a stand, companies would have to pay more. It really is that simple.