"Bush" is a term from the 20th Century British Colonies (various bits of Africa, India, so on) with a meaning equivalent to "wilderness" or "jungle." The basic meaning is any undeveloped land. This does NOT mean virgin, untouched land, but rather un-Westernized land. Thus it means isolated, poorly maintained or neglected areas - or perhaps even including well-maintained "primitive" areas.
Aircraft considered well suited to "Bush" flying tend to be light, robust, and easily maintained, typically with large cargo capacities (for their class) and good short field performance, mainly because of the various conditions of undeveloped land (such as tight landings and ascents from small areas, rough ground, and long travelling distances).
Size and construction are thus quite important for bush planes. Smaller aircraft are more likely to possess the needed power-to-weight requirements and short-field performance than larger aircraft. They can also operate off of smaller stores of fuel, so they can be made to travel quite far off of less input. Light composite construction works great for most ordinary flying - and even for some aerobatics - but performs quite poorly in demanding, turbulent environments and does NOT absorb impacts (especially from sharp objects) very well. However, some larger aircraft may be suitable. For instance, a properly handled C-130 works as a good bush-plane (and it's even better with JATO bottles on the back!). However, you will probably Never see an Extra 300 or any tubeliner 600 miles into the Alaskan forest or deep in the jungles of Africa! For very similar sets of reasons, there are not that many helicopters that fly into the bush.
However, there are some exceptions to all rules. The Russians provide a lot of them. Their Antonovs, Mils, Kamovs, and so on provide some counter examples. Heck, they even have a tube built for bush flying in the form of the Yak 40! There are also a number of other American designs, like the Chinook, Blackhawk, and so on.
