I have found many fully translated pieces of Esperanto literature, but I am still a beginner, so these are difficult for me to understand. Therefore I am now looking for texts comprised of both English and Esperanto. Preferably one translation on either side. Do such texts exist, if so, where do I find them?
There is a nice side-by-side English and Esperanto version of Alice in Wonderland here.
Check the libroservo, the book selling service, at any Esperanto event. I'm sure the libroservisto will be delighted to help! I bought my copy of The Day We Became Cyborg / La Tago de Kiborgiĝo at the JES. It is a bilingual book with the side-by-side English and Esperanto versions you are looking for.
It can also be found in an online shop here: http://espero.sk/index.php?akcia=zmenjazyk&jazyk=EO