Firstly let's talk about terms.

The Bible isn't a monolithic entity. Religiously it is, but that's a theological topic. What it is for historians is a collection of at least 66 books (in the Protestant version) written by different authors at different times in different settings. So talking about 'the Bible' isn't that helpful in actually using the Bible for historical study (unless we're studying the history of how 'the Bible' was used and treated like a single entity, but that's a different study).

Secondly, let's talk about sources. What's a source? It's a something that tells you about a something. Sources aren't 'proof'. They're more like witnesses. The more witnesses you have, and the more cohesive they are, and the more corroboration you get, the more probable your conclusions can be. The less witnesses you have, the less certain you can be about your conclusions.

Of course the Bible is a valid source. In the sense that it's a collection of historical documents open to, and useful for, historical inquiry. In my experience, people who make this claim generally have a poor understanding of what the Bible is, and a poor understanding of historical study. The fact that the Bible is a product of religious people means it has bias. But all texts have bias. Bias in itself doesn't make something less reliable or less useful, it just means you need to read it with an awareness of bias. This is equally true for other historical documents. It's true for modern history textbooks. It's true for writing about the Bible. Excluding texts from study because of one's own presuppositions is not good historical practice.

To address your two specific "if" questions, the claim about Plato is generally a claim about manuscript attestation and historical witness. Plato's writings survive in 7 main manuscripts, with the earliest dating to ca. 900 AD. This tells you that the manuscript evidence for, say, the New Testament is more numerous and earlier than that for Plato. It doesn't tell you which set of texts is more 'historical', but it does mean claims about the New Testament being subject to massive revision and written many hundreds of years later are severely dubious.

The issue with enslavement of Jews in Egypt and the Exodus event is that there is no direct corroboration. All other evidence fails to support the narrative of this episode that Exodus supplies. Depending on how you see the rest of that evidence, you might conclude that there is positive evidence it didn't or couldn't have happened. Again, it's not about 'proof', it's about weighing up evidence, data, and witnesses, and decided what is most probable.

edit: grammar.