How can I seal between siding and sunroom to block bee access?
It's possibly "duct seal", a flexible and sticky material sold for plugging cable entrance holes. If so, you can add more over the top. You'd work it into a rope by rolling it between your hands, then press it in place. 

It could also be some sort of tube caulk. Since it doesn't appear to be silicone you should be able to bond to it with either duct seal or caulk.

A better fix might be to scribe-fit a thin trim board to the siding. You'd do this by tracing the siding using a spacer, then cut to fit with a jigsaw or similar.