Do Gold Coins Of Bactrian King Menander Exist ?

There wouldn't be electrum. By the time of Menander (160-145 BC), electrum had long-gone as a coinage metal - anyone making gold coins was making them of pure gold, not heavily diluted with silver (though I think the Celts may be an exception to this).

Menander's boss throughout his reign was Eukratides (171-135 BC), and gold coins are listed in Sear for him, including a unique 20-stater piece (168 grams, or nearly 6 ounces!). If that piece is listed, then any gold coins for Menander which might have been known when Sear was last revised (1998) would also have been listed, too. No listing means none were known. I suspect Eukratides kept the right to make gold coins for himself.

What would they look like if they did exist? Well, Eukratides' gold coins have the Dioscuri on them, so they might look something like Bobby's Roman one here, only gold.