Update by @unknown: This affects multiple mobs.
Affected mobs (keep updated):
Villager
Chicken
Cow
Pig
Sheep
Wolf
Ocelot
Mooshroom
Silverfish
Spider
Cave Spider
Zombie
Zombie Pigman
Original report: Ocelots will jump up and sit on chests as normal. However, when they jump onto a bed to sit on it, they just keep jumping up and down on it and alternating between sit and stand positions in the air. Playing iOS release.
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Confirmed!

Confirmed on Android and Win10 (Samsung Galaxy S4 Android 5.0.1 and on Asus B121 Win10Pro) both running MCPE 0.12.2
When a cat (tamed ocelot) move onto a bed, it will constantly jump alternating sit/stand positions when in the air. I expected the cat to be on the bed sitting or standing but not jumping constantly.
Note 1: if you press sit while any pet is falling, they will revert to standing. That works as intended.
Note 2: if you press sit right as the cat is landing on the bed, it will sit and stay sitting on the bed. Timing is everything. If you then press stand, the cat will stand on the bed without constantly jumping.
The bug appears to be in the AI for what happens when a cat gets on a bed. It should be compared to the AI for what happens when a cat gets on a chest (which worked properly on both my devices).

Confirmed on Samsung Galaxy Tab 4. 0.13.0.

Confirmed for version 0.14.0 build 5
Device Samsung Galaxy Note3 Android 5.0

This was happening to me as well in 16.0, I didn't realize it was a bug. Tamed ocelots were jumping on my bed as well as a "pet" chicken I was keeping in my house.
Device: iPhone 5s, iOS 10

Appears to be fixed in 1.0.0.