Looks like you may have misunderstood. How many items are in your catalog? Do you even need a database for this?
Lets run with you do for arguments sake.
You should have two recordsets. One rsGolfUmbrella that you already had, and another for rsGolfUmbrellaColors... Then you should be populating the list in the add to cart form from the second recordset using the "Dynamic" button in the properties panel.
But really you may not need a recordset... would it work if you just used:
<form name="sumidrive1_15_ATC_<?php echo $row_rsGolfUmbrella["golfId"]; ?>" method="POST" action="<?php echo $_SERVER["PHP_SELF"]; ?><?php echo (isset($_SERVER["QUERY_STRING"]) && $_SERVER["QUERY_STRING"] != "")?"?".$_SERVER["QUERY_STRING"]:""; ?>">
<input type="hidden" name="sumidrive1_15_ID_Add" value="<?php echo $row_rsGolfUmbrella["golfId"]; ?>" >
<input name="sumidrive1_15_Quantity_Add" type="text" class="qtyformelem" value="1" size="4" >
<select name="sumidrive1_15_Color_Add">
<option value="Black" selected="selected">Black</option>
<option value="Navy">Navy</option>
</select>
<input name="sumidrive1_15_ATC" type="image" class="cartbutton" value="Add to Cart" src="/assets/misc images/cart.gif" alt="Add to Cart" border="0">
</form>
