Equivalent ternary operator for constexpr if?

No, there is no constexepr conditional operator. But you could wrap the whole thing in a lambda and immediately evaluate it (an IIFE):

template<typename Mode>
class BusAddress {
public:
    explicit constexpr BusAddress(Address device)
     : mAddress([&]{
          if constexpr (Mode::write) {
            return device.mDevice << 1;
          }
          else {
            return (device.mDevice << 1) | 0x01;
          }         
        }())
     { }
private:
    uint8_t mAddress = 0;    
};

It may not be the sexiest code ever, but it gets the job done. Note that lambdas are constexpr by default where possible as of N4487 and P0170.