I grew up in a town that is exactly between New York City and Philadelphia and therefore had a house marked as the place where George Washington slept in between the two capitals. This is the “ancient” history of United States. Of course in other countries in Europe and certainly in Iraq and Egypt (where stories of the Bible actually happened) and China there is much more of an ancient history to a actually see. But I don’t think there is a place like Israel in its connection to the Bible.
I can’t speak about all Israelis but I would think that most Israelis and especially those who make aliyah feel the awesomeness of living in the land of the Bible – the promise land. I personally live in the area where Avraham certainly lived or walked through, where David fought Goliath, where the Maccabees hid, where the ancient city of Betar existed, where Rachel was buried as well as Adam and Eve, Abraham and Sarah, Isaac and Rivka, and Yaakov and Leah are buried (and I have to tell you I live in the land that is “contested” but consistently seen Jews over thousands of years.) When I remember this (which traveling and looking over the land) I personally am moved by the entirety of it.
There are halachos that affect us because we live in Israel opposed to any place other else. We must be careful of the agricultural laws which only are commanded to keep in the land of Israel. Most of what we keep is still not under all the qualifications as if it was directly commanded from the Bible. Until there is a majority of Jews living in Israel it is not considered fulfilling all the qualifications, yet we still keep them. Laws like orla, maaser, shemittah, pe’ah, and more.
There is a feeling (maybe only among religious Jews) that we are living in the synagogue and our behavior, dress and language should reflect that. When you are home or in a place of worship; you do behave differently. In Israel and more so in Jerusalem we are closer to the holy Temple and we feel there is a need to be more careful.
The fact that we can go to the Wailing wall which stands so close to the original Temple is emotional for most Jews especially the first time they ever see it. The roads we build are usually based on the roads of long ago.
I find, especially just after visiting outside of Israel; the contrast becomes vivid. There is a permeance of spirituality a person if interested they can tap in. It is easier to recognize G-d’s providence in Israel more than anywhere else.
Growing up in America I was aware of a long period of time that separates the day from the night. The period of dusk could last an hour. (I am sure there are real figures for this) Here in Israel, dusk is very short. There is day. Than there is night. I feel Israelis are affected by this in their thinking. It is either black or white – very little gray. It does cause volatile opinions and discussions. The effect in Israel is everyone has an opinion which has been sharpened by much discourse. Or maybe it is the effects of the yeshivah world which arguing is the mode of learning.
In anycase, to sum up, Yes, the Bible does affect everyday living in Israel; if you want it to.