How to apply Bootstrap dropdown style to an ASP.NET MVC DropDownList?

It is very much possible, and really easy. Please Read:
DropDownList bootstrap styling

All you need is:

@Html.DropDownList("movieGenre", "All", new { @class = "form-control"})

or

@Html.DropDownListFor(model => model.MovieGenreModel, SelectList, new { @class = "form-control"})