What you're essentially dealing with here is an impedance mismatch. Your bass is a high-impedance device and since your mixer accepts only low-impedance signals at the line-in, there will be a tonal forfeit. Generally you'll notice a difference in the top and low ends of the signal in a case such as this. The XENYX 802 will indeed put out a balanced line level signal at the mixer outputs (which should not be plugged into a mic preamp, but a LINE IN), and in that way it becomes a pseudo-DI, but remember that a DI is a device that accepts a HIGH-IMPEDANCE signal, which it then converts to a LOW-IMPEDANCE signal to be accepted by a mic preamp. All of these aspects affect tone.
Cheers