How to Bind a Dropdown from a Web Api in JQuery

First define your service model

  public class Busstopmodel
    {
         [Key]
        public int BUSSTOPS_ID { get; set; }

        public string BUSSTOP_DESCRIPTION { get; set; }

        public string BUSSTOP_COORDINATES { get; set; }

        public string BUSSTOP_SEARCH_NAME { get; set; }

        public string  message { get; set; }

        public DateTime ARCHIVE_DATE { get; set; }
        
    }

and here is a function that gets data from the DB

public List<Busstopmodel> GetPlaces()
        {
            string StrCon = ConfigurationManager.ConnectionStrings["DefaultConnection"].ConnectionString;
            SqlConnection connection = new SqlConnection(StrCon);
            SqlCommand command = new SqlCommand();
            command.CommandText = "spx_getplaces";
            command.Connection = connection;
            command.CommandType = CommandType.StoredProcedure;
            SqlDataAdapter da = new SqlDataAdapter();

            List<Busstopmodel> lstplaces = new List<Busstopmodel>();

            DataTable dtplaces = new DataTable();

            da.SelectCommand = command;
            try
            {
                connection.Open();

                da.Fill(dtplaces);

                if (dtplaces.Rows.Count > 0)
                {
                    for (int i = 0; i < dtplaces.Rows.Count; i++)
                    { 
                        Busstopmodel m = new Busstopmodel();
                        
                        if(dtplaces.Rows[i]["BUSSTOPS_ID"] != DBNull.Value) 
                             m.BUSSTOPS_ID = Convert.ToInt32(dtplaces.Rows[i]["BUSSTOPS_ID"]);

                        if (dtplaces.Rows[i]["BUSSTOP_COORDINATES"] != DBNull.Value)
                            m.BUSSTOP_COORDINATES = dtplaces.Rows[i]["BUSSTOP_COORDINATES"].ToString();

                        if (dtplaces.Rows[i]["BUSSTOP_DESCRIPTION"] != DBNull.Value)
                            m.BUSSTOP_DESCRIPTION = dtplaces.Rows[i]["BUSSTOP_DESCRIPTION"].ToString();

                        if (dtplaces.Rows[i]["BUSSTOP_SEARCH_NAME"] != DBNull.Value)
                            m.BUSSTOP_SEARCH_NAME = dtplaces.Rows[i]["BUSSTOP_SEARCH_NAME"].ToString();
                        lstplaces.Add(m);

                    }
                }
            }
            catch (SqlException ex)
            {
                throw ex;
            }
            finally
            {
                connection.Close();
            }
            return lstplaces ;
            
        }

Write a code to retrieve this method in your controller

  // GET api/values
        public IEnumerable<Busstopmodel> Get()
        { 
            TolaTaxiService.Services.Database.Database db = new TolaTaxiService.Services.Database.Database();

            IEnumerable<Busstopmodel> busstopmodel = db.GetPlaces();

            if (busstopmodel == null)
            {
                throw new HttpResponseException(Request.CreateResponse(HttpStatusCode.NotFound));
            }

            return busstopmodel;
        }

calls this in JQuery when the page loads

   <script src="Js/jquery-1.11.0.min.js"></script> 
    <script type="text/javascript">
       

        $(document).ready(function ()
        {
            e.preventDefault();
            var data = [];
            $.getJSON("http://localhost:39192/api/Values", null, function (data) {
                data = $.map(data, function (item, a) {
                    return "<option value=" + item.Value + ">" + item.Text + "</option>";
                });
                $("#Select1").html(data.join(""));
            });
        });