Double bass and contrabassoon are exceptions. They do sound an octave lower than written, but that is so they don’t have an absurd number of leger lines. I don’t think of them as actually being transposing instruments because, while it may be displaced by an octave, a written C still sounds as a C. But that’s just me. 
At least that’s better than Baritone/Euphonium where the “fingerings” (pitches) get displaced by a 2nd (9th, if you prefer)!
Please, everyone, it seems that I’ve driven this discussion well off topic. I thank you for the education but it’s time to return to the OP’s query! 
At the risk of adding to what @jaskarbong just said—and I was just about to point out the same thing—I must add one more comment (but just one!).
Well, that might explain the use of bass clef for bass clarinet as well. Here are two ways to notate C2 for a (transposed) bass clarinet in B-flat:
or 
Which is actually easier to read? I’ll grant for the sake of the argument that players prefer the former, but that only justifies treble clef in the part. As a conductor, reading the former in a full score is simply awkward.
Returning to @jaskarbong 's point, it’s unfortunate that most of us have taken OP’s very legitimate request and, rather than even attempt to answer it, have basically told him that he’s wrong to even ask.
Except in German notation, which sounds a major second lower in either bass or treble clefs.
And then there’s Rite of Spring, where Stravinsky uses German notation for bass clef but French notation for treble clef.
Double bass in solo tuning sounds a minor seventh lower than written, and when horn is written in bass clef it can transpose either up or down!
up to 5 ledger lines is daily business (flute, violin, horn, [contra]bass tuba).
The treble clef notation of the bass clarinet is more “clarinet-ish” and there are max 4 lines down unlike 5 and more up in bass clef.
(Okay, one more comment…)
Other than the horn, those instruments aren’t transposing (even on just an octave)—and when the horn does get that low, even it usually gets a bass clef. Also, excessive leger lines in the other instances call for an octave line in the usual direction (up for flute and violin, down for tuba). If we used a down octave line in bass clarinet, that’s essentially taking the transposition down to two octaves.
And if we’re translating between written and sounding, bass clef goes from one leger line to two in my previous example, whereas treble goes from four to eight (!). So, I maintain that bass clef is easier, especially since a bass clarinet is usually on the low end rather than the high.
Speaking of the horn, it seems that the preference for treble clef stems from thinking of the instrument as a “Clarinet in B-flat basso” by analogy with horns—merely another transposition of essentially the same instrument, rather than an essentially different instrument.
Finale forced me to do just that!
No, absolutely not. If I see this note written in a transposed part …
… it is exactly the same fingering whether I’m playing a Clarinet in Bb, a Clarinet in A, or a Bass Clarinet. If I see that note written for Alto or Baritone Saxophone, it is the exact same fingering on either instrument. If you are asking Bass Clarinet players to play in bass clef, you are asking them to associate a different fingering with a different note, which is much more challenging than reading a few ledger lines.
It’s sort of the same reason why you should never use 8va for Flute parts (at least until D7). Woodwind players are used to looking at a note and immediately associating it with a fingering. We’ve practiced this our whole lives and do it without thinking about it. On a Piano you can just shift your hands an octave and use the same fingerings, but on woodwind instruments an octave or clef change means you often have to use completely different fingerings.
I’ve admittedly done almost no historical work in my 30+ years as a professional copyist/composer/arranger. Oddly enough, one of the few historical things I’ve done is a set of Bass Clarinet transcriptions, mostly just transposing Bassoon and Cello pieces for Bass Clarinet. (Treble clef, up a 9th) I’ve copied for dozens of well-known composers though, including two Pulitzer Prize winners, and I’ve never been asked to put Bass Clarinet in bass clef ever. Nor have I done so in my own writing. Bass clef is fine for a concert pitch score, like in film work, and If you want to adhere to historical conventions for historical work, fine, but bass clef is never used for Bass Clarinet parts in new work.
Amen!
From the player’s perspective, there are four notation systems they can encounter in order of prevalence:
- French notation (Treble Clef only - sounds down a major 9th)
- German notation (mix of Bass Clef and Treble Clef, both sounding down a major 2nd)
- Russian notation (Bass Clef sounding down a major 2nd, Treble Clef sounding down a major 9th)
- Italian notation (Bass Clef only and Treble Clef, both sounding down a major 9th).
No modern player wants to see their part using notations 2, 3 or 4, but seasoned orchestral players will be able to read them (the difficulty is working out which is which from context). Modern use of these systems should be restricted to urtext engravings of older works that make use of them; all new works should use the French notation system for the player’s part.
From the conductor’s perspective, if the score is transposing, show the Bass Clarinet staff in the same notation system as above, ie. French by default, but German/Russian/Italian if creating a urtext edition.
If the score is in concert pitch, it is usually preferable to use Bass Clef from the bottom of the instrument (sounding Bb1/Db2) up to about sounding G4, then Treble clef for the rest of the range. Both clefs should sound at concert pitch, and not displaced by an octave.
As a former professional clarinetist (also bass) I’d get pretty pissed at a composer that handed me anything but treble. First I’d curse, then I’d transpose. Just 'sayin