con una sonrisa tirando a amarga

[Stu]

, con una sonrisa tirando a amarga

A search shows sonrisa amarga as a bitter or ironic smile, which makes sense but why " tirando a" . I assume amarga is an adjective so it just does not seem to fit.

[Rusty]

Yes, 'con una sonrisa amarga' would be translated as 'with a bitter smile.'
The smile in what you posted isn't bitter yet, but it's getting there.
'With a somewhat bitter smile' or 'with a smile turning bitter' would be a good translation.

[Stu]

Ah! Very good
Thank you

[Tomisimo]

This usage of "tirando" can often be translated colloquially with the "-ish" suffix.