The core of your question is whether you need your own router or if you can just bridge your network to another network and use their router. And the answer to that is yes.
Either way will usually work. When you are bridging you essentially become part of their segment, so you have to request a DHCP address from their router, for example. If you set up your own router then your router becomes a device on their segment (using a bridge as above) and then your own network is behind your router on your own segment with your own IP address range and your DHCP requests go to your own router instead of theirs. Either way will work.
Thanks for the information. Rather than purchase a bridge I would rather just keep my existing USB antenna and effect the bridge between that and the router with the notebook. Obviously my existing USB antenna (built-in hardware) would be incompatible with any bridge I would purchase and necessitate the need to also acquire an external stand-alone antenna.
With regards to the actual bridging in the network configuration control panel are there any potential hardware conflicts that I should be aware of?
Would I expect to see any sort of signal or quality degradation with respect to my average speeds I reported earlier with such a network setup?
Thanks for the reply as it was very informative.