There is no Eb2...unless you have a fiver or tune down. An Eb3 does not suffice in many tunes where a low Eb repetition is called for.
For some songs the octave up is fine and playing in Eb, standard tuning is great.
You're off by an octave, friend. Maybe you forgot bass guitar is a transposing instrument that sounds one octave lower than written?
Eb2 is at the 11th fret of the E string, or the 6th fret of the A string, or the 1st fret of the D string (on a standard tuned EADG bass).