A University lecturer said that one of her students uttered this one. This is a mashup of “bridge the gap” (make it easier for two groups to communicate with each other) and “straddle the fence” (not to take a side when presented with two or more options). “Fences” and “bridges” are often mixed up, apparently. See, e.g., https://malaphors.com/2016/11/28/theres-a-lot-of-mending-bridges-going-on/
A big thanks to K. Carver for hearing this one and passing it on!