You need a spell checker.
You talk about a fluorescent lamp, then go onto calling it a bulb.
Assuming it is a fitting with four 4' tubes, that quite a hefty fitting.
What you don't say is what the wattage is, what sort of system it is, glow starter or electronic ballast, so it's mainly guesswork.
Conventional fluorescent tubes are being phased out in favour of LED "tubes" which give better lighting and are cheaper to run.
I wouldn't mess about with what could be complicated and hazardous, possibly 4 wires per tube wiring.
The original lampholders can be replaced, but you will end up with terminal blocks and plenty of scope for error.
Remove the old fitting completely (power off) and you should be left with a live/neutral/earth cable supply.
Find a nice LED ceiling fitting to match the light output of the old tubes and wire up according to instructions.
LED lighting comes in different colours from warm white to daylight or 2700K to 6500K.
I personally like the cool white or daylight LEDs for good colour rendition.
Keep the old tubes? No chance
