I have been watching experienced runners who can kill the elder dragon without the lava bucket, can anyone tell me how to do this when I only have 1 piece of obsidian?

just one cycle normally and prayge

You could always try the delt cycle

What is the delt cycle?

search minecraft bedrock psg and the cycle in it is called delt

Or u can do three bed no lava

its called rng cycle for a reason
you have to be fast+have good timing, obviously
but the 2nd thing is rng, most of the time it just doesnt work cuz the dragon goes the wrong way, or something weird happens (most of the time)

Do u know what the real odds for RNG cycle are cause I want to get a good 1.18.30 time