Does using Trumbeak's "Mountain Pass" Ability count as playing it from the hand? If so, would it be blocked if my opponent used Chimecho's "Bell of Silence" attack on the previous turn?
No, it is not being played from the hand. You are revealing the Trumbeak and then putting it into the Lost Zone; that is not blocked by Bell of Silence.
Source: TPCi Rules Team (2018-11-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM4_43
SM8_165