I am trying to join the information from a line to that of a point associated with that point. To explain a bit, it would be adding the information from a bus line to the associated bus stops with that line. The bus stops are not touching the line, so I was thinking about running a buffer to capture the bus stops, but some of them are very close to another and that would potentially add the wrong line information to the wrong point.
To deal with the irregularity of stops close to the associated bus lines, I would as Kingfisher suggests use the "near" tool in Arcgis Pro to calculate the XY coordinates of your start point and closest line intersection (In case you do not want to manipulate your input points, have a look at "generate near table).
Afterwards, use the "xy to line" tool to generate a line between the start point and end point, if you want to calculate lengths.
One other tip, if you want to make sure that your joins are connecting to the correct lines. I suggest looking into the tool called "Calculate Geometry Attributes" to calculate the start or end point of a line (which you can then use for a spatial join, matching with the right side of the line).