I use DropdownListFor()
Which has a slightly different approach I use a model not a view bag. A model is a separate class called by the Controller. An example is given in this stack overflow
c# - MVC ViewModel example - Stack Overflow[
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For this to work in your model you need 2 properties.
public List<SelectListItem> items {get;set;}
public int MyAssignedToValue {get;set;}
then in your view
@Html.DropdownListFor(a=> a.MyAssignedToValue, Model.items)