Traveling from Belize to Nicaragua via ferry or bus.

https://belizebus.wordpress.com/
His site is pretty current, and gives you options all the way to San Pedro Sula. San Pedro Sula is a pretty major transportation hub and I'm sure once there you won't have any problems finding buses southward.
I would try and coordinate to get to Puerto Cortes from Belize (less frequent service than to Puerto Barrios) but it will eliminate the Guatemala border crossing.

I'll be watching your responses with interest.  I, too, need to travel south to Panama.  The only info I can lend is from a friend named Iris, who used to live in Guatemala, and who moved herself and her family from Guatemala to Panama.  They moved by bus.  It took them two weeks.
According to Google Maps search that did a couple of years ago, it should take only 3 days.  I do not know if they were calculating a non stop trip or not.  But there's your range.  Anywhere from 3 days to 2 weeks!  Yeck!  And I understand you have to be very careful through much of Central America.

Thank you Brigitte. I will add this resource to my arsenal of options for exploring. I know some of the direct transportation option. The blog you provided has additional insight to organizing every leg of the trip.

I am elated to learn San Salvador to Antigua, Guatemala and back is possible in one day.

I am still reviewing my options for Belize. I may add flying into Cancun then bus to Belize for a few days, while continuing south via commercial bus or guagua. I only have 6 days for exploring Belize and every north of Nicaragua.

This trip is an initiation for experiencing new places. Sequential trips will allow me more time to immerse myself.