I'm arranging a piece where the electric bass plays a low Eb on the recording. I think it's probably unfair to expect a bass player to perform in an alternate tuning just to appease this demand. Should I write the Eb up the octave instead?
There is a big difference in the sound of the lowest Eb on a 4 string bass and an Eb an octave lower so if that is the sound you want go after it. As a bassist if I know someone wants that note or any note lower than an E I will do one of three things:
If I’m playing 4 string and I need an Eb or a D for a song or two I drop my E string down to a D which can be done manually or by a special E string tuner with a lever that does it on the fly. Playing the low string tuned a step below isn’t much of a stretch for an experienced player and some guys who have the lever are completely comfortable with it.
Another option is to tune the entire bass a half step down and transpose up a half step. This is a little more cumbersome say in a live setting but doable if there is time for the transition or if a bassist brings an extra instrument for that purpose.
The other option already mentioned is of course a 5 (or 6) string bass with a low B string. 5’s have become very common and most pros own at least one and are comfortable playing them. Many times I will even choose to bring a 5 to a gig or recording because I want to have those extra low notes available to me.
I would consider, if the low Eb is really important, one of the following options:
You can simulate the "depth" of a low Eb by playing the higher Eb with the Bb a fifth up from it (i.e. an "Eb power chord") on the bass. My experience is that this is more effective on more mellow bass tones- think "tone knob rolled all the way down", and it still sounds a bit different than a single note. Still, if you want the low Eb to be a dramatic moment, this could work.
You could arrange the piece to be played one half step higher than the original recording, and then the bassist would need to play a low E- which is clearly not a problem.
Consider how important the low Eb is in the arrangement you're doing, and also who is going to play it. If they have a 5-string electric bass with low B string, then a low Eb is no problem. You could mark both Eb's on the score to let the player know they have the option (or perhaps little bit of text to say play down 8ve if possible).
Laurence Payne's answer is the best one. If you need a low E-flat, write it that way and make the bassist go out an get a 5-string (good excuse for buying a new fiddle anyway) or play it an octave higher accompanied by the fifth above. Changing key will change the tonal character of the piece and it might not always be exactly what you are after. Retuning the bass down a half-step is also a terrible idea (especially for a gigging musician who uses charts) because then you have to carry around another bass or transpose everything else that does not require a low E-flat on the fly.