Both prokaryotic and eukaryotic organisms contain DNA bridging proteins, which can have regulatory or architectural functions. The molecular and mechanical details of such proteins are hard to obtain, in particular if they involve non-specific interactions. The bacterial nucleoid consists of hundreds of DNA loops, shaped in part by non-specific DNA bridging proteins such as histone-like nucleoid structuring protein (H-NS), leucine-responsive regulatory protein (Lrp) and SMC (structural maintenance of chromosomes) proteins. We have developed an optical tweezers instrument that can independently handle two DNA molecules, which allows the systematic investigation of protein-mediated DNA-DNA interactions. Here we use this technique to investigate the abundant non-specific nucleoid-associated protein H-NS, and show that H-NS is dynamically organized between two DNA molecules in register with their helical pitch. Our optical tweezers also allow us to carry out dynamic force spectroscopy on non-specific DNA binding proteins and thereby to determine an energy landscape for the H-NS-DNA interaction. Our results explain how the bacterial nucleoid can be effectively compacted and organized, but be dynamic in nature and accessible to DNA-tracking motor enzymes. Finally, our experimental approach is widely applicable to other DNA bridging proteins, as well as to complex DNA interactions involving multiple DNA molecules.