What is the "official" stances of Reformed Baptists on Dispensationalism?
What biblical base do they claim for such views?
If, as a group, they would generally not teach Dispensationalism, are there aspects of it viewed as biblical?
This video is very helpful at seeing the overlap and distinctions between Reformed Baptist theology and Dispensationalism.
First of all, you'd have to define Reformed Baptist. I prefer to define it as someone who holds to the 1689 London Baptist Confession. The LBCF1689 is a covenantal confession which by definition rejects dispensationalism.
It's hard to boil down into a small post the biblical basis for 1689 Federalism (covenant theology), but it is based on letting Scripture interpret Scripture, especially the New Testament as a fuller revelation of the Old. It also recognizes the typological relationship between Israel and the Church.
As with most systems, there is some overlap of good material. Dispensationalism rightly recognizes some of the problems with traditional Paedobaptist covenant theology, for instance, but their "solution" ultimately goes much too far.