Remember when St Paul said in his letter to Timothy that a deacon is to be the husband of only one wife. That means in the early Church, there were men with more than one wife.
I think that verse is a little more complicated, since it refers to not only simultaneous bigamy but serial bigamy as well. The early witness of the Church was that upon baptism all had to give up multiple wives, though as late as Jerome it appears that polygamy prior to baptism was still looked at as valid
1 Tim 3:12 and 1 Tim 3:2 (on bishops and priests) is usually taken to refer to the irregularity of bigamy. I marry, my wife dies, I remarry, my 2nd wife dies...I coulud not be come a priest. See even sucessive marriages is bigamy (successive as opposed to simultaneous)
This is not just the medieval understanding, but that of the Fathers as well. The only disagreement being whether marriages prior to baptism counted. It is a strange thing that an irregularity for Holy Orders that stems from the 1st century no longer exists as of 1983
And therefore he first places what pertains to chastity, saying "a man of one wife." Likewise in Titus I. But in this there is seen a disagreement between Augustine and Jerome.
For Jerome says that this is understood after Baptism, since if before baptism a man had had two wives, or one first, and the other afterward, he is not impeded from ordination, since through baptism all is wiped away.
Augustine and Ambrose say otherwise, since whether before or after, if a man had two wives, he is not ordained.
But does not Baptism wipe away all things? I respond, yes in respect to sins, but no in respect to irregularity, which at times is incurred without any sin from ecclesiatical institution alone. But marriage is not a sin even among Pagans.
But what is the cause of this institution? Does it not rather impede he who has many concubines? I respond. It must be said that this is made not because of incontinence only, but because of the representation of the sacrament, since the spouse of the Church is Christ and the Church is one, "one is my turtle-dove." (Canticles 5) [Taken from St. Thomas Aquinas, In I Tim, cap. 1, lec. 1]
Note that a man who is married, commits adultery numerous times, and whose wife dies, did not incur the irregularity of bigamy. As far as that when he could be ordained (if his sin was notorious then there was another irregularity though)