Expeditious Retreat uses a bonus action to cast and grants you the ability to take the Dash action as a bonus action for as long as the spell lasts.
So, can you use the Dash it grants you when cast in the same turn as you cast Expeditious Retreat or is it only in subsequent turns?
You can only take a single bonus action each turn. However, Expeditious Retreat says that:
When you cast this spell, and then as a bonus action on each of your turns until the spell ends, you can take the Dash action.
This can be paraphrased as:
When you cast this spell, you can take the Dash action. Then, as a bonus action on each of your turns until the spell ends, you can take the Dash action.
Or to summarise, on the turn you cast the spell, no further action beyond casting the spell is required to take the Dash action.
Yes.
Expeditious Retreat has a casting time of a bonus action, and it gives you the ability to take the dash action as a bonus action (normally you are only allowed one bonus action per turn). However, it explicitly states you can take the dash action when casting (i.e. on the same turn you cast the spell). Since you can always take the dash action as an action, this implies that you get your extra speed this turn as well.
You can also take the dash action as an action on your turn, should you so choose. This is always an option, and is not changed by the spell.
The benefit of this spell is that on subsequent turns you can take both an action and bonus action dash to triple your movement speed. This gives 90 ft of movement for your average character, and potentially 480 ft of movement for a Monk 14 / Barb 5 / Wizard 1 with the mobile feat and boots of speed (although this character wouldn't really have a use for the spell, since monks already get a bonus action dash by spending a ki point).
Expeditious Retreat spell description
This spell allows you to move at an incredible pace. When you cast this spell, and then as a bonus action on each of your turns until the spell ends, you can take the Dash action.
