This bug report is a parity issue with Java.

Summary:
In the Java version, bees try to pollinate wither roses, despite the damage they take (but ultimately fail to pollinate them). In the Bedrock, bees easily pollinate withered roses and may not even get the wilting effect (unless someone sticks them into the flower).

I believe that in the Java version this is done more correctly than in the bedrock, since wither roses are poisonous.

Update from version 1.19.60:
Since version 1.19.60, bees fly too low to the wither rose and die due to the wither effect. (Also, if you push the bee a little away from the flower, it will not die and will be able to pollinate the flower.)  They do not fly away when receiving a wither effect and normal flowers do not take priority.

Steps to Reproduce:

1. Plant a wither rose flower.
2. Summon a bee near the wither rose or lure it to him.

Observed Results:
The bee will fly to the flower and start pollinating it.

Expected Results:
The bee flies towards the flower, gets a wither effect and flies away from the flower. (will try to pollinate it, but then it will fly further)

Videos:
Java Java_1.16.mp4
Bedrock Bedrock_1.16.mp4

Note:
MC-159365 - breeding bees with wiser roses conceived function

Also, in the Java version, a bee has priority over a regular flower, and in the bedrock, it doesn't care what flower is in front of it (wither rose or any other).

Bee priority video:
Java: Java bee priority.mp4
Bedrock: Bedrock bee priority.mp4