I have a line feature that represents the route that a shuttle bus will travel and a point layer that represents all of the spots where the shuttle will stop. I am not looking to find an optimal route between the stops. The route that the shuttle will take is pre-determined and is not necessarily the shortest or fastest route. How can I create a network that will follow my route and output the time and distance between stops? The goal is to estimate the total route travel time in each directions and the time between each points so we can create a daily schedule with timepoints.
If I understand your requirements correctly, you should be able to take your existing line feature that represents the bus route and create a network dataset on it. That is, turn it into a network. Then use the Route solver to solve a route between the stops in order of visiting them. Then thing you will need is some cost attribute on the line feature that tells how much travel time it takes to travel along that line.
If you want to calculate the travel time along some existing street network (presumably to account for real road and traffic conditions), you could export the vertices of the existing bus line feature (try the Feature Vertices To Points tool) and use all the vertices as "Stops" in a Route analysis. You'd get way more stops that you really need, but it should ensure that the calculated route follows the desired path. If you include both the vertices and the real Stops as Route analysis "Stops" (sorry for the confusing terminology), you can still check the arrival times for the real Stops in the final output and use that for your timing, ignoring all the dummy "Stops" (the vertices).
Not sure if I explained that well...