Here comes one of the more challenging aspects of Reform Judaism: the Bible isn't literal truth. Reform Jews consider the Biblical record to be more along the lines of a collection of legends and folk tales meant to teach a moral or cultural lesson. Think more along the lines of George Washington chopping down the cherry tree than Abraham Lincoln delivering the Gettysburg Address.
On with the show.
Even though Israel and the Holy Land are among Earth's hottest archeological hot spots, we can prove very few events recorded in the Bible. We're talking about some stunners, too. There's no evidence of King David. Shocking, right? Same with Moses. In fact, there's no evidence of the Exodus from Egypt.
Since the Rabbi did his doctoral dissertation on the Exodus, we spent a lot of time talking about it. We really have no idea when it happened, if in fact it did. There are no references to it in any known Egyptian texts.
We do know that there were Semites in Egypt in about 1700 BCE. They were called the Hyksos, but their documented story is very different from the Exodus story. They were kicked out of Egypt in about 1600 BCE. Not quite "let my people go". Additionally, some of the places that the Hebrews wrote about during their 4o years of wandering have been found. There's no evidence of an encampment. Even some of the towns that were settled shortly after the return to Canaan have been excavated; they didn't find any artifacts that had Egyptian influence.
It gets pretty interesting when you carefully analyze the writings about the Exodus. It seems that the Tribe of Judah was not involved. They don't claim that their people were enslaved until after they start identifying themselves as Israel. In their separate, nationalistic, identity, there's nothing. Even people from the other Tribes leave them out. It seems like a Tribe that's represented by a lion and known for their warrior ways would have done something worth mention.
After the Exodus came the battle of Jericho. Despite what Joshua recored, the walls didn't fall. There's not even evidence of the city having been occupied at that time. In fact, there's no evidence of the conquest of Canaan. See Israel Finkelstein's The Bible Unearthed (I haven't read it. Rabbi mentioned it. I do know that he was on Digging for the Truth, in the King David episode).
Speaking of David...
There's only one shred of reference to his existence, other than the Bible, and that's the Tel Dan Stele. It's esstially a stone tablet, and one line reads "Beit David", which translates to "House of David". It would be pretty convincing evidence, if only there were enough information to link that line to the Biblical King. Alas. All we can prove is that there was a King named David (This was also in Digging for the Truth).
In the end, you have to choose your path. You can either have faith that the entire Bible is true and the science is fallible, or you can trust the science and understand that people have a tendency to exaggerate, especially when it comes to "my God can kick your God's ass".