"It is about time for me to go."
Translation:Mae'n hen bryd i fi fynd.
Yes, amser does mean time, relating to the time of day and a period of time. Time in the general sense.
eg Amser cinio - dinner time; amser coffi = coffee time.
Pryd = time or an occasion
The literal translation of this is 'It is old time for me to go'; this is sometimes transposed to English as 'It is high time for me to go'
The translation proposed here is hopefully a less formal than the 'high time' to convey the meaning that it's time to go from wherever the speaker is.
'Hen' is one of the few adjectives that comes before a noun and causes a soft mutation.