Ceacht 16:
bhí	was, were	v.	
bhí sé	he was	[v.] + [pron.]	
bhí siad	they were	[v.] + [pron.]	
ag ithe	eating	“ag” + [vn.]	
ag ól	drinking	“ag” + [vn.]	
ag imeacht	going off	“ag” + [vn.]	
ag fanacht	waiting	“ag” + [vn.]	
ag rith	running	“ag” + [vn.]	
ag imirt	playing	“ag” + [vn.]	
seo!	here!	{pron. / determiner}	
réidh	ready	adj.	
i mo dhiaidh	after me	[prep.]+[poss.pron.]+[n. #len.#]	
is dócha	probably	copular phrase	
fáilte romhat	you're welcome	verbal phrase	

bhí (was): This is the past tense of the irregular verb bí .  Originally, the past tense of a verb was formed by placing do in front of the verb and this do causes lenition of certain consonants.
You may still see some older texts where it was written as "do bhí" but in today's Irish this do is omitted, leaving just the lenited verb - hence we see "bhí". 

Having said that, one still forms the past tense of a verb which begins with a vowel by placing do in front of the verb where it gets shortened to d'.

"i mo dhiaidh" means literally "in my afterness" i.e. behind me.