Beans are a warm season crop. They need temperatures over 60 degrees to germinate and prefer a little warmer than that. I looked up the soil temperatures in Oakland County in early May, and the ground temperatures were still below 60 degrees. Yes, a planter may be a different temperature than the ground, but I would still suspect that the poor germination was due to low temperature.

The bean plant in the picture looks healthy and it appears there may be flower buds starting on the lower part of the plant. Roma beans have pole and bush varieties, I’m not sure what variety you planted. If this is a pole bean yes, it is short, but for a bush bean it could just be a late germinated plant. Bean plants can also vary widely in size.

As far as producing fruit a few things can cause a bean to not set fruit. Too much nitrogen fertilizer can cause a plant to grow a lot of nice green vegetation and not flower. Beans can fix their own nitrogen and adding a nitrogen fertilizer can overdo it. Also, very hot weather (above 85) can slow production or cause flowers to drop.

I am including a few links here. The first is the link to enviroweather showing the soil temperatures for the first part of May in Oakland County.

The next two are bulletins on growing beans in Michigan.

https://legacy.enviroweather.msu.edu/run.php?stn=cmc&mod=w_sc&da1=1&mo1=5&da2=9&mo2=5&yr=2022&mc=397&ds=cd

https://www.canr.msu.edu/resources/how_to_grow_beans_part_1

https://www.canr.msu.edu/resources/how_to_grow_beans_part_2