One switch connects to two routers

A wireless bridge connects two routers over Wi-Fi, letting devices share one internet connection without long Ethernet cables. Now as far as I know a switch does not do network translation and this won't work with one IP address. So I bought two addresses at my ISP. Is there any. One alternative depends on the type of router that this is. If this router is one of those then the solution is simple - connect each of the switches to a switch port (configured in the same vlan). [pdf]