Looking for a part of the Bolivian jungle that is nearer to the North of the country and relatively easy to get to (by flight or maximum 8-hour-ish bus ride)
I consider the area of Rurrenabaque (= Rurre) to be the only answer to your question.
From Rurre you can do rain forest or pampas tours.
You can also visit forest and rain forest elsewhere in Bolivia. For instance the Cotapata National Park is relatively close to La Paz.
El Jiri Ecolodge http://www.jiribolivia.com is close to Coroico and from there you can walk in the forest of the Cotapata NP.
I (we) visited El Jiri Ecolodge / Refugio in August 2010. Ten days before we had similarly been in the rain forest near Rurre and in the Madidi National Park, but this did not influence our adventure here in Cotapata, we enjoyed it.
You use the word jungle. To me jungle is the rain forest. But I know that some also use the word about the pampas north / north east of Rurre.
The word pampa / pampas means plain. The type of landscape / ecosystem (and variants) is called prairie, steppe and savanna in other parts of the world. almost 6 years ago