The exact nature of Zoroastrian influence on Second Temple era Judaism is actually a fairly contentious issue in both Biblical and Zoroastrian studies. I've only seen a small handful of scholars, typically on the more conservative end of Biblical Studies argue that there is no influence at all, but exactly which influences are very much up for debate (which you'll find with even a cursory glance over the many, many articles that come up when you search for Judaism Zoroastrianism on an academic search system like jstor.org)

Apocalypticism is no different. You can find discussion of a range of positions in this wittily named article by Domenico Agostini, specific focus on Daniel in this recent book from Vicente Dobroruka, and a discussion of both possible Zoroastrian and Hellenistic influences from Dobroruka here.

Ehrman is correct that there is relatively little Zoroastrian literature dated to before the exile, and the examples we do have dated to that period and earlier, Zoroastrian scripture known as the Avesta, only reached its current form around the 5th Century CE. However, analysis of both the Avestan language and the culture described within agree that the content itself was likely composed orally between c.1000-500 BCE, give or take about 200 years on either end. There is minimal evidence for any sort of Zoroastrian (or even generally Iranian) literature dated prior to the Sassanid Persian Empire (224-651 CE) and most of that is now lost. One surviving early Sassanid text, The Letter of Tansar, does suggest that written records were viewed as a poor substitute for memorization, especially in religious matters, which at least partly explains the lack of sources.

The earliest surviving religious commentaries, such as the (Greater) Bundahishn and Denkard, which provide detailed explanations of Zoroastrian eschatology are dated to the 7th-9th Centuries, or later in the case of some specific sections. However, Ehrman's dismissal of these later sources belies references to the end times in the Avesta. These references are often obscure and hard to pick out in easily available translations, partly because they are not the focus of most of the surviving Avesta. The surviving Zoroastrian scripture is primarily made up of hymns and prayers, often dedicated to a particular divinity in their pantheon.

However, the Zam Yasht does dedicated significant space to describing the end of time, conventionally known in Zoroastrianism by the name Frashokereti meaning "making excellent." Additional direct references to either the term or the events of Frashokereti can be found in the Frawardin Yasht, Yasna 24, Yasna 62, and Vendidad 18.3. The explanation in the Zam Yasht also makes it clear that the messianic figure known as the Saoshyant was already associated with Frashokereti as well, and he and his future deeds are referenced in several other sections of the Avesta.

All this establishes is that Zoroastrian eschatological thought was circulating by the time of the Jewish Exile in Babylon and their return under Achaemenid Persian rule. It is not clear how much of the modern Avesta was widely circulated under the Achaemenids, though many sources (Persian, Greek, and otherwise) make it clear that many of the same beliefs expressed in the Avesta were already established.

There is no Jewish source that explicitly states that they borrowed ideas from Zoroastrian priests or the like, though interestingly there are early Christian writings to that effect. Justin Martyr's Apologia I, Clement of Alexandria's Stromata VI, Lactantius' Divinae Institutiones, and the anonymous Theosophy all cite The Oracles of Hystsaspes as a genuinely inspired prophetic text. The Oracles are generally understood today as Hellenistic or Roman period pseudepigrapha, but the content referenced does align broadly with Zoroastrian eschatology and the aforementioned authors seem to believe it to be a genuinely ancient Iranic text.

As for Second Temple Judaism, there are enough similarities from both the Avestan and later descriptions of Frashokereti with Jewish apocalypses to support an argument for some level of influence. The demon Asmodeus, featured in the apocryphal Book of Tobit by the Greek name Ἀσμοδαῖος (Asmodaios) and the Talmud under variants of the Hebrew אַשְמְדּאָי (Ashmedai), is often believed to be a transliteration of the Avestan Aeshma-Daiva, or a Persianization of the same, a Daiva (false god or demon). See here for both citation and a generally relevant article. Once again, not direct proof of an apocalyptic connection, but a sign of influence more broadly.

Personally, I am skeptical of any claim that Jewish apocalypticism stems directly from Zoroastrianism. The (proto-)apocalyptic elements of many texts typically dated to the period of the exile itself, or immediately before or after, shows that the basic concepts were already circulating before extensive contact with Zoroastrians, as discussed here. There also is not enough detail in the Avestan sources to firmly establish all of the necessary elements in Zoroastrianism at that point in time. I would lean more toward a co-development process given the available information.

For more information on Zoroastrianism and Iranic history in general, Encyclopaedia Iranica is an excellent, free resource. I referenced several articles in writing this response:

• SAOŠYANT
• HYSTASPES, ORACLES OF
• AVESTA i
• BUNDAHIŠN
• DĒNKARD
• FRAŠŌ.KƎRƎTI
• ZAMYĀD YAŠT