Have you set BearShare to have clearance in your software firewall? Giving it total UDP and TCP clearance for whichever ports it is using? If not, open your firewall control panel and choose Add program to the safe list.

You might need to port forward your connection device. It probably has NAT firewall which is partially blocking BearShare. If you wish to do this, go to Port Forwarding Guides Listed by Manufacturer and Model - PortForward.com and find your model of modem/router, then click the model link. Click the skip advertisement on next page, then look for BearShare on the list of programs and follow the instructions given. Then BearShare should be 100% all clear for connecting.
ie: the 5.1 version did not have UPnP support, which is a process that requests a modem/router to open a port whilst the program is running.