“Does the Bible support a geocentric or heliocentric view of our little part of our galaxy?”
Well, the Bible supports both and neither… sort of! “Huh?!”
Since the biblical writers approached the processes of nature “phenomenologically”, meaning according to what they observed around them, the Biblical writers themselves did literally “view” the universe from a geocentric, or “earth-centered”, perspective, believing the earth to be the center of what astronomers now call the “Solar System” (because, well, they generally believe our neck of the woods to be a “system” of planets surrounded the sun. “Heliocentric” means “sun-centered”.) See Joshua 10:12-13; Ecclesiastes 1:5; Psalms 19:6-7; 93:1; 104:5 for examples of the Bible’s phenomenological perspective of the universe as geocentric.
However, the Bible does not teach this phenomenological geocentric understanding as scientific truth, in modern terms. Increasingly, trustworthy modern Bible scholars see the Bible’s purpose not as intending to teach material origins in modern scientific terms that make claims that should fit with contemporary models of chemistry, biology, physics, e.g., but as intending to teach functional purposes, i.e., God’s purposes for the world. This doesn’t mean the Bible has nothing to say about material origins or nature and God’s role and purposes in it, but simply that the Bible wasn’t written to give us an account of the earth’s material origins in a way that fits with modern scientific theories and categories.
And, btw, these scholars make such arguments from the text and context of the Bible itself. For example, many modern Old Testament scholars now talk about Genesis 1 as not teaching material scientific origins regarding how God made the world, according to our modern understanding, but as teaching functional origins of why God made the world. This is the difference between (a) saying a chair is a chair because it is made up of metal/wood/material parts that go together to form what we call a chair (i.e., material origins) and (b) saying a chair is a chair when those parts comes together (because an intelligent designer puts them together, btw!) to form something on which we can actually sit, i.e., it ‘becomes’ a chair when we can sit on it and it does its job. This is like when God says, in Genesis 1, that the things He was creating were “good”, meaning they were carrying out the purposes for which He made them.
So, I would say it is perfectly okay, not contrary to Scripture, and fully reasonable to believe in the modern scientific understanding of our little part of the Milky Way as a heliocentric (“Solar”) System.