The question as posed is in two parts:
"Do you think that living for a year without God is a reasonable way to go about discovering the truth? One of your responses to your friends indicates that living out a certain way of life is a good way to confirm what one already thinks is true. However, is it a good or reliable method of discovering the truth?"
The first part of this question is asking whether Bell's experiment was a reasonable way of discovering the truth about whether God exists or not. My short answer to that question is: No.
The second part of this question is asking whether it's a reliable way of discovering truth. My short answer to that is: Maybe. It depends on what kind of truth you want to discover.
1. Not all truths are falsifiable by experience.
For example, if I were to live for a year under the assumption that our Vice President, Mike Pence, is my best buddy who goes for beers with me at the local bar every weekend. That is something that could (and would) be falsified by my experience of life. I've never met the man before, didn't vote for him, am not a member of his political party or a donor to it, don't have any friends who can introduce me to him, and I doubt he'll respond to my messages asking to have a beer with him now that he's busy with performing the role of the Vice President of the United States. It would become very quickly obvious that my assumption was incorrect.
On the other hand, a proposition like "the contents of scientific theories describe reality as it truly is rather than reality as filtered through our perceptual mechanisms" isn't really susceptible to that sort of falsification because it's not a proposition we could falsify by living as if it's true for a year. Similarly, a proposition like "there is a ground of being from which all that exists gained its existence and sustains its existence and we call this God" isn't susceptible to being falsified by living a year as if it were true.
So if people want to do "a year with ________" or "a year without ________" experiments to discover a truth, it's important that they actually choose a truth that can be falsified (or at least made significantly more or less probable in light of a Bayesian analysis) by means of doing that experiment. Ryan Bell didn't really consider experimental design effectively when deciding to live for a year without God, obviously.
2. Cognitive biases always tilt us toward thinking we've confirmed what we assume.
When we live as if something is true for a significant period of time, it gives our confirmation bias lots of opportunities to work its magic. One of the byproducts of that is that we find all sorts of new reasons to believe whatever proposition it is.
And because of the familiarity principle, the more we expose ourselves to the phenomenon of living this way, the more we appreciate it and enjoy it, as long as there aren't direct and obvious negative consequences to doing so that we can't explain away by way of confirmation bias. Add into the mix that in this process, we will generally seek and find a community of people who believe it as well, and then normal emotional attachments, groupthink, and the in-group bias we all suffer from will tend to keep us on that path.
Atheists often (correctly) point out that tendency to rationalize whatever it is you already believe when looking at how many people share the religion of their parents. Rationalizing what we already believe or how we already behave is a perfectly natural consequence of how our brains work. And that remains true once we change those beliefs. Our brain picks right up and rationalizes our new belief in the same way.
I've often noticed that new believers (whether a new skeptic or new Christian) don't have good reasons that they can articulate for their new belief. Those good reasons and good arguments tend to accumulate over a number of years of thought and dialogue rather than actually being the primary driver of the change in belief.
Of course, another byproduct of living as if something were true is that we understand better the position of those who hold what we commit to living out as true. And that's quite valuable. I've found it to be valuable, at any rate. That seems to me to be the better reason for living for a time as an atheist, or a Buddhist, or a Christian, or a Muslim, and so on. It would be a valuable way to understand those with whom you disagree. That said...
In the end, it's not reasonable to live a year without God as a means of deciding whether God exists or not because it's not the kind of proposition that can be tested that way. And it's not reliable because of the outsized impact of our normal human tendency to rationalize whatever it is we are currently doing on our conclusions about what's true.