Unfortunately, it wasn't translated too well, in my opinion. To be fair, they didn't really have that many other options.
Maybe it was because at that time, the writers may not have expected the anime to air outside Japan yet. Which might have caused some language barriers when the dub translators translated it to English but I thought the 'cowterpie' thing was really irrelevant because Ash's Caterpie had already evolved and also about the pun, 'bug' doesn't even close to 'cow'.
Sugimori art used; quote from Omega Ruby and Alpha Sapphire Banner created by me
Altaria, Mario, Pokémon Emerald, Route 110 Theme (RS)
Images from Bulbapedia, Banner from upload to Imgur