In my recent post on Ignatius' Christology, Esteban Vázquez asked in a comment:

I wonder if there are any studies out there of St Ignatius' knowledge of the Acts of the Apostles, and what text of it he might have known.

I thought I'd respond since I've done a fair bit of tracking references between the NT and the Apostolic Fathers. I don't have any specific studies on Acts to refer to, but I do have some hints on tracking this stuff down. Here we go.

1. Editions of the Apostolic Fathers (Holmes, Ehrman, Lake and Lightfoot at least, perhaps others) typically have reference indices in the back. Several of these editions cite cross-references in the margin or in footnotes. The Logos Bible Software editions of Holmes, Lake and Lightfoot index these references, so information on any cross-reference is a reference search away. For example, I have an "Apostolic Fathers" collection, I just searched it for "bible in 'Act 20' " to search for references to Acts 20 (any verse). This is a great place to start. The references won't all be quotations/allusions, and the reference may just be topical—but it is a way to get a quick look at what the editions have to offer.
2. The original 1905 edition of The New Testament in the Apostolic Fathers is online at archive.org. You could (and should) examine the portion on Ignatius' writings. There is a scripture index in the back, though I don't know if it is comprehensive. Acts 20.28 is not referenced in the index. I find this one so valuable (see some previous work here; hopefully I'll pick up that work again sometime soon) that I have it printed out and on my desk. Do read the front matter to understand how the book works, though.
3. The 2005 two-volume edition of The New Testament in the Apostolic Fathers (amazon.com) should also be consulted. Mine is downstairs and I'm upstairs on the computer in the office ... and I'm lazy ... so I'm not going to check it right now. Maybe later. But this should be on your list of stuff to check, definitely.
4. If you can find a copy, you want to check Biblia Patristica. But it can be hard to find. So good luck.
5. Hermeneia has commentary editions for Didache, Ignatius, Shepherd of Hermas and the Apostolic Traditions. A reference search of the Ignatius volume turns up the following:

What enflames the Ephesians is “the blood of God”—that is, the blood of Christ. The expression is found in important manuscripts (SB) of Acts 20:28. Tertullian also says that we are bought with a price—the “blood of God” (sanguine dei; Ad uxor. 2.3.1). That “God” suffered (see Rom. 6.3) was acceptable language before criticism required some refinement of the conviction that God (or God’s Son) had become man and died on the cross. Monophysites were later to appeal to precisely such unreflective remarks of Ignatius in defense of their christology. By the term “blood” Ignatius has in mind the passion (Phd. inscr; Sm. 6.1) and/or the eucharist (Phd. 4). Such a reference is appropriate in this context since the eucharistic blood (Tr. 8.1; Rom. 7.3) and the blood of the passion (Sm. 1.1) are both closely linked with “love” by Ignatius (see Introduction, 5.7).
Schoedel, W. R., Ignatius, S., Bishop of Antioch, & Koester, H. (1985). Ignatius of Antioch : A commentary on the Letters of Ignatius of Antioch. Includes indexes. Hermeneia—a critical and historical commentary on the Bible (42). Philadelphia: Fortress Press.

Lastly, there are several specialized volumes that may come in handy, depending on what you're looking for and how easily you can get to a good library that might actually have them on the shelves. Use the footnotes in the new 2-vol NTAF as a roadmap (amazon.com); they are well worth following. If Ignatius, or Clement, or Polycarp, then see if you can find Lightfoot's multivolume editions (two vols on Clem, three vols on Iggy and Polly). Also, if First Clement, you need to locate Donald Hagner's work on OT & NT quotations in First Clement; it is a gold mine.

Finally, if you're dealing with a specific NT book or subcorpus (e.g. Pastoral Epistles) then commentaries are hit and miss. Again, go to a decent library and check out some technical commentaries, you may strike gold. FWIW, on the Pastorals, I've found the Yale Anchor Bible Commentary volumes (L.T. Johnson on 1&2 Timothy; Jerome Quinn on Titus) and Hermeneia the more valuable ones when it comes to references to the Apostolic Fathers and other early Christian writings; but other volumes in those series may vary. I'd expect Quinn & Wacker on 1&2 Timothy in the Eerdmans Critical Commentary to also be good in this realm (though perhaps not so good in other realms).