If I understand correct: your script-tool is supposed to create and populate a field that you will later buffer with? You problem is that when you are creating the model, you want to select the buffer distance from field option, but it is not showing up. It appears blank because the tool has not run and the field does not yet exist in the dataset.
You can create a dummy output or copy your data, then run the model ( which runs the tool) to create the field. The model will stop at the buffer tool because it can't go further without knowing which field you want to buffer from. Hopefully then you can complete the model and it will work fine for future iterations.