The fundamental disagreement between coherentism (to which Bonjour is but one — quite influential — contributor) and foundationalism is, at its root, the justification for knowledge.
Bonjour's disagreement, much the same as most coherentists, lies in the foundationalist belief (in the general sense, as there are different types of foundationalism) that all inferential knowledge must ultimately derive from some non-inferential belief/justification (which one is a point of debate).
Here, "inferential knowledge" means knowledge derived from something else. Roughly:
I have inferential knowledge P if I know E and I know that E makes P probable.
As you'll notice, this poses a regression problem for knowing E, and the foundationalist solution is to place epistemic priority in non-inferential knowledge, which in general terms means knowledge that does not depend on me knowing (or inferring from) some other knowledge, and which is infallible. The common foundationalist way of saying this is:
I have non-inferential knowledge P if my belief in P necessitates that P is true.
Note that there is some debate about this definition, but that is another question.
Now, Bonjour's coherentist disagreement with this idea is that the perceived regress used in foundationalism is actually not a problem. He argues (as you've summarized) that justification for a belief lies in its coherence with some standard of belief (in this case, our own system of beliefs). This system need not satisfy the foundationalist property of non-inferential knowledge, because coherentism takes it as epistemically valid by itself. Thus, roughly, Bonjour would assert the following:
I have knowledge P if P is coherent with my system of belief S
Coherentism does not require that S be non-inferential in the foundationalist sense, because it takes S as reliable by virtue of it being a valid system of belief. Of course, there is quite a bit of debate on just what it takes to validate any system of belief S, but non-inference is generally not a criteria for such validation.
Thus, Bonjour's coherence theory separates it from foundationalism in that he rejects the foundationalist problem of regression and its solution of non-inference, instead defining a system of belief as the source of epistemology.
I would strongly recommend the SEP's articles on Foundationalism and Coherentism for further reading.