The wheels on the little fold up bike probably has much smaller tires than your new road bike. Bigger tires = more unwieldy, more awkward, more difficult to steer, much faster. Also, possibly the position of your fold up bike and the position of your new road bike is different. Maybe you are now in a more plank like position on your road bike compared to a more upright position on your prior fold up bike? More upright on your prior fold up is usually less scary then the more aerodynamic lower position of your new road bike.
I think you just need to ride your new bike more, preferably on your own first. I still remember how scary and uncomfortable it was when I went from my hybrid to the road bike. I made sure than my stem was as high up as possible so that I could be more upright on the road bike. Then, as I got more used to the road bike, I lowered my stem 3 times. As you get more comfortable on your new bike, you can pick up more speed. When you are "fast enough", then bike with the BF.
Also, as Sky King stated, maybe you can go up one width size on your road bike tires? That will also help you feel a tad more stable and less bumpy.
2014 Liv Lust
2013 Specialized Fate Expert with carbon wheelset (sold)
2012 Specialized Amira Elite
2010 Santa Cruz Juliana with R kit and Crampon pedals (sold)
2011 Specialized Ariel Sport,suspension post,Serfas Rx Women's Microfiber saddle (sold)