Summary: Recently Mojang/Microsoft/Minecraft Released 1.18 Experimental Snapshot 1 and 1.17.10 both containing the ability for Lush and Dripstone Caves to Generate Naturally in Minecraft Bedrock or Java. If a player were to take the time in both versions to find a Dripstone or Lush Cave you might notice in Minecraft Bedrock you may have to load multiple seeds and go a few thousand blocks I had to load ten seeds and go 2000 blocks on average in each seed to find one Dripstone and Lush Cave in Minecraft Bedrock. However it should be noted I only went in one seeds 150 blocks to find one Lush Caves and 250 blocks to find a Dripstone Cave both in the same seed if I were to find two cave biomes I would have to load from my testing 15-20 seeds and go 2500 block in each one.

Methods to Reproduce:

Method 1:
Step 1: Download 1.18 Experimental Snapshot 1on Minecraft Java.
Step 2: Download 1.17.20.21 or 1.17.10.0 on Minecraft Bedrock.
Step 3: Create World and Locate Lush Cave and Dripstone Caves on Java.
Step 4: Create World with Caves n Cliffs Toggle Enabled and Locate Lush and Dripstone Caves on Bedrock.
Step 5: Repeat.

Method 2:
Step 1: Look up a Minecraft Bedrock and Java Lush or Dripstone Cave Seed.
Step 2: Load the Seed or World.
Step 3: Repeat.

Observed Result: Lush Caves and Dripstone Caves are 133.3333333333334x Rarer to Find on Minecraft Bedrock Edition on Average.

Expected Result: Lush Caves and Dripstone Caves on Bedrock need to be 133.3333333333334x Easier to Find.

Note: In Further Testing I Had to Create 30+ Worlds to Find One Lush Cave.

Update: Dripstone Caves Rarer Than Java and Lush Caves Slightly or 20% More Common Than Java.