public class FooViewModel
{
    // other properties

    public int SelectedBarId { get; set; }

    public IEnumerable<SelectListItem> BarOptions { get; set; }
}

public ActionResult CreateFoo()
{
    var model = new FooViewModel();

    PopulateBarOptions(model);
    return View(model);
}

[HttpPost]
public ActionResult CreateFoo(FooViewModel model)
{
    if (ModelState.IsValid)
    {
        var foo = new Foo
        {
            // map over other properties from model here
            Bar = db.Bars.Find(model.SelectedBarId)
        };
        db.Foos.Add(foo);
        db.SaveChanges();
        return RedirectToAction("Index");
    }

    PopulateBarOptions(model);
    return View(model);
}

protected void PopulateBarOptions(FooViewModel model)
{
    model.BarOptions = db.Bars.Select(x => new SelectListItem { Value = x.Id.ToString(), Text = x.Name });
}

@Html.DropDownListFor(m => m.SelectedBarId, Model.BarOptions)

Bars = db.Bars.Where(x => model.SelectedBarIds.Contains(x.Id))

@Html.ListBoxFor(m => m.SelectedBarIds, Model.BarOptions)

// remove deselected items
foo.Bars.Where(x => !model.SelectedBarIds.Contains(x.Id)).ToList()
    .ForEach(x => foo.Bars.Remove(x));

// add newly selected items
var existingBarIds = foo.Bars.Select(x => x.Id);
db.Bars.Where(x => model.SelectedBarIds.Exclude(existingBarIds).Contains(x.Id)).ToList()
    .ForEach(x => foo.Bars.Add(x));