At level 22 in Diamond and Pearl and level 18 in Platinum/HeartGold/SoulSilver.
However, if you evolve it into Prinplup first, it is at level 24 for Diamond and Pearl and level 19 for Platinum/HeartGold/SoulSilver.
Also, there's no reason to use a TM for Bubble Beam when you can teach it much more powerful attacks like Surf later on.
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Piplup learns moves such as Growl, Bubble, Water Sport, Peck, Bide, Bubblebeam, Fury Attack, Brine, Whirlpool, Mist, Drill Pick and Hydro Pump.
Wartortle doesn't learn Bubble Beam naturally, but you can teach it with TM11 at any time.
Piplup learns Peck at level 15
Hydro pump, Strength, Skull bash, Surf, Subbmishion, Sesmic toss, Water gun, Bubble beam, Bubble, Withdraw, Mega punch
rattata does not learn bubble at all, there isn't even a TM for bubble