The first definition of ‘two-bit’ makes its etymology obvious: it is derived from the noun ‘two bits.’ However, ‘two bits’ is an interesting phrase because it actually means ‘the value of a quarter of a dollar.’
There is no such thing as a single bit, at least not anymore. The now obsolete Spanish dollar was composed of eight reals, or eight bits, so a quarter of the dollar equaled two bits.
The phrase ‘two bits’ carried over into U.S. usage, though there’s no bit coin in U.S. currency.
‘Two bits’ first appeared in print in English in 1730 (and later developed the figurative sense of ‘something of small worth or importance’), followed in 1802 by its adjectival relative. These days, though, the adjective has far surpassed the noun in popularity.