The phrase "a bit of dedicated" is not correct in English as it is incomplete and lacks context.
It could be used in a context where you are referring to a small amount of dedication or commitment to something, but it needs to be part of a complete thought.
Example: "I need a bit of dedicated time to focus on my project."
Alternatives: "a little dedication" or "some commitment".
Following the opening episode, in which the latter accidentally eats a bit of mămăligă dedicated by Stan to those who honor God, Satan himself condemns his subordinate to service the peasant.
He tries to get a bit of football banter going, dedicating "AKA... What a Life!" to "the Manchester City supporters in the house", prompting half-hearted chants of "Blue Army".
With a bit of funding, entrepreneurs can dedicate time to building the earliest versions of their products or services, and get some initial traction with their first users.
Antonio Hart had already worked through a number of different styles -- bebop with a free time feeling, powerhouse rhythm-and-blues, a bit of gospel -- but a song dedicated to the recently deceased pop-jazz icon Grover Washington Jr. gave him the opportunity to take his set in yet another direction.
IGN's Jason Bates noted that the Thief II display attracted "a bit of a buzz and a small crowd of dedicated onlookers".
These instructions suffer from a bit of Engrish but it's nothing a dedicated hacker can't figure out.
Portable Hard Drive, however, includes a dedicated keypad for adding a bit of James Bond fun to the process of encrypting — and decrypting — your data.
Mr. Wallace (not to be confused with the CBS News correspondent) is a dedicated government man, and there is a bit of fantasy in the book.
Corporate songs enjoyed a bit of a boom in the 1990s and a decade ago a website dedicated to collecting them acquired a short-lived cult following.
Slimmy defined the album as "freedom, with a bit of "teasing" and "sexual", an album full of strong songs dedicated to his fans.
