Can an oxygen sensor be bypassed instead of having to replace it on an '89 Honda Accord?

You could, but your engine will enter 'limp mode'. Simply unplugging it would do the trick.

The O2 sensor is vital for a fuel injected car to determine proper mixture. Without it, the car defaults to a 'best guess' that is usually richer than needed. This will reduce your gas mileage considerably, may make it lurch and stall, and could do other bad things like burn valves. Spring for the O2 sensor. Including buying the socket to fit it, it'll run you between $60 and $150 guessing. $80 is probably about right for the Honda. I think it's a three wire on the accord.

Side note.. you can test an O2 sensor yourself pretty easily.

If it's a heated type sensor, the one wire that's a diff color is usually the signal wire. The sensor actually produces a small voltage while in operation. Keep in mind it needs to warm up to be accurate.. about 600 degrees. Drive the car for 5 min before testing.

With a DIGITAL dvm, test the voltage produced on the signal wire with respect to ground. In circuit it should bounce right around .45 volts. If your getting around 12 volts or 0 volts, you got the wrong wire. When the mixture is rich it will read higher, lean lower. When I say bounce, I mean that it will not stay at .45 volts, but swing wildly up and down around it, but stay close to .45 as the center. The engine is dynamically updating the mixture, causing it to lean out, then go rich alternately and the signal from the O2 sensor will reflect this balancing act. The voltage produce should always stay in the range of .1 volts to .9 volts.

This applys to 1 wire, or 3 wire O2 sensors. The 3 wire versions have a heated coil of wire to get the sensor up to operating temp faster. 4 wire versions I assume have a separate ground for the signal. It may be possible to figure out what goes where by process of elimination. (find the 12 volt, find the 0 volt, the other two are likely the signal wires.)

A Digital voltmeter is required to keep from blowing things up as their input impedence is high enough to not affect the signal.

Enough for now.

You can bypass it by simply unplugging it. However, your check engine light will always be on and you won't be able to pass an emmissions test.

Also, if you unplug your oxygen sensor, the car will probably shift harder (if it has an automatic transmission) and it won't shift correctly when you try to accelerate at speeds over 30 MPH (it will downshift too many gears).

You can buy OEM replacement oxygen sensors on the internet for around $80.00. I would recommend NKG or DENSO brands.