TL;DR - Using Mordenkainen's Tome of Foes, you can use Fey Step while wild shaped. If you don't have access to this sourcebook (or your DM doesn't allow it), you can't.
If you do have access to Mordenkainen's Tome of Foes, you can use Fey Step while transformed.
In the ToF (p.62), Fey Step is described as requiring only a bonus action to activate.
Fey Step. As a bonus action, you can magically teleport up to 30 feet to an unoccupied space you can see. Once you use this trait, you can't do so again until you finish a short or long rest.
According to the PHB (p.67), a wild shaped druid can neither talk nor cast spells, but can otherwise use all it's racial and class features, unless physically unable to in his new form. As "using a bonus action" is not prohibited by wild shape, a ToF Eladrin druid should be able to use Fey Step while under the effect of wild shape.
If you do not have access to Mordenkainen's Tome of Foes, however, you cannot use Fey Step while transformed.
Outside of the ToF, the only mention of the Eladrin subrace is in the DMG, where it is used as an example of a subrace that could be created by a DM. While the ToF should take precedence over the optional variant rules found in the DMG, not all tables will have access to the ToF, or even allow it. In this context, and only in this context, should the rules found in the DMG prevail.
According to the variant rules found in the DMG (p.286), the Eladrin "Fey Step" racial powers allow them to cast the misty step spell, which requires a verbal component.
Once again, according to the PHB (p.67), a wild shaped druid can neither talk nor cast spells. So while you do retain the Fey Step racial feature, you cannot use it when using the DMG's version of the Eladrin.
The only exception to this is if you are an 18th level druid with the "Beast Spells" class feature, which allows you to cast spells while transformed.