Q. Catholics claim that their bishops date all the way back to the Apostles, but I don’t see any evidence of this. Do they have any historical records?
A. Yes we do! Catholics believe the Pope is the local Bishop of Rome, as well as the Supreme Pontiff. In light of that, the line of Popes that go all the way back to St. Peter is proof of Apostolic Succession. Besides the numerous writings of the Popes, which are so many that I dare not list them all here, there is also a list of the Popes at the Vatican City (click on the attachment for full view).
And here is a full list of the Popes, with antipopes as well:
Regarding the writings of the Popes, many, but not all of them, can be found online:
1 Peter: vatican.va/archive/ENG0839/__P121.HTM
2 Peter: vatican.va/archive/ENG0839/__P127.HTM
Papal Encyclicals: papalencyclicals.net/popelist.htm
If you want more papal writings, you can write to the Vatican, since they are in the Secret Archives. It is worthwhile to note that every nation, including Vatican City, has its own secret archives, and that certain archives are opened after many years after a person’s death - while others are only opened by request, due to the delicate nature of either the content or the paper on which the content is written (some of the books in the Secret Archives are so old that if you touch them they’ll crumble to dust). You can write to the Vatican here: vatican.usembassy.gov/Vatican/Writing.asp