How does grad school view a consistent B average in a course sequence?
Although this might be a showstopper for some specific schools), this need not be a show stopper in general. Especially if you have at least one very strong letter of recommendation.  My answer is based on the assumption that you would apply for CS or statistics, which are just tangential enough to be able to pass muster from most people's point of view.

It could be more harmful if the B sequence were exactly aligned with what you're going to apply for.  But it isn't.

(There are of course other ways to increase your chances, e.g.: don't apply late; if there's a subject GRE required, a strong score here could help; get some feedback on your essay draft.)