I believe that it is Diplocarpon rosae fungus ( Rose Black Spot). The fungus is plant specific to Roses, so it is unlikely to infect other plants.
I don't think that I have ever used Bayer's BioAdvance Rose and Flower, however I don't like garden products that are 'all in one' types. I have found that products that claim to do more than one thing, such as fertilize and prevent disease, don't do either of those things very well and often contain chemicals you don't really need. These products can also seriously over fertilize your garden. If you apply too much chemical fertilizer all at once, even in outside, in ground gardens, the fertilizer can still cause 'fertilizer burn' to plant roots.
An 'all in one' product seems more convenient, but it isn't in the long run. It is best to get separate products (fertilizer, fungicide, insecticide) tailored to the specific needs of your garden and plants.
To control the Rose Black Spot on your roses, you are going to need a good commercial fungicide. When I absolutely need to use a commercial fungicide, I generally like Safer Brand fungicide or Daconil fungicide. Whatever fungicide you choose, make sure that it has Rose Black Spot listed on the label as one of the fungal diseases it treats.
Good garden hygiene, such as the removal of infected leaves, leaf litter and pruning off diseased stems (back to healthy wood) is also a very important part of treating any fungal disease, including Rose Black Spot.