Would it be safe to use a 0.065 bass string as a B string(tuned to Bb) on a 7 string guitar with a scale length of 26.5?
You can look up string tensions in the D'Addario String Tension Supplement, however your scale length is not covered in their tables.
They do, however, provide a general formula
T (Tension) = (UW x (2 x L x F)2) / 386.4
.. where UW is the unit weight in lb/in, L is the scale length in inches, and F is the frequency of the note in Hz. Presumably if they used metric measures, there wouldn't need to be a fudge constant.
The unit weight of their 0.065 string is 0.0007956
So the tension of your proposed string is:
0.0007956 * (2 * 26.5 * 58.27)2) / 385.5 = 19.68lbs
That's comfortably in the range you'd expect of an electric guitar string, so should work fine.
To work out the ideal string to go with your other strings, work out the tension for your other strings, and use the formula in the opposite direction to find the unit weight that gives you B♭ at that tension:
UW (unit weight) = (T x 386.4) / (2 x L x F)2
The low Bb (the 7th string I'm assuming you'll tune lower than your open Eb right? The Open A is 110Hz); so… Bb is .5 X 116.5Hz (58.25Hz actually, recheck the chart on the D'Addario string site).
This changes the math of course… 0.0007956 * (2 * 26.5 * 58.25)2) / 386.4 = 19.62lbs… It's just about right, if you want to go totally "Gonzo" tune it to an Ab (1 finger barre power chords in the two low strings, bwhahaha!!! fast), seriously… you can also do low I-V bossa/samba bass lines with a single finger if you tune your 7th down a 5th instead of a 4th.
Ab would be 0.0007956 * (2 * 26.5 * 51.9)2) / 386.4 = 15.57lbs
As a comment on detuned 7-string playing… you might want to consider a little heavier on the bottom end than a standard set of "10's", sometimes the 6 & 7 strings can get a little "floppy" and if you press too hard (especially with jumbo frets), you can get intonation problems (sometimes things just get a little too loose, but the 26.5" scale should help, just mentioning it so you're aware of it). I used to use a set of "11's" with a plain third, and it was over a decade ago, I've forgotten what I used for a low A string (55Hz, I didn't normally detune).
Given that your bottom E is .046", a .060" or .062" will do the job. A .065" will maybe give a little more grunt to your sound, but would feel a little tight. That string rarely gets bent, so it doesn't need to be too loose. Any thicker than .065" won't do the neck any favours in the long term.You mention 'bass string'. An ordinary guitar string will be better, as a string for a bass guitar (if that's what you mean) is way too long. I'm not sure if the make-up of a .065" guitar string is any different from a .065" bass guitar string - probably not. Just shorter.When you have a successful set-up, please let us know: theory is all very well - practice is better.
Leaving aside the fact that anytime someone asks "[is] it safe," I start thinking about escaped Nazi officers posing as dentists :-), I would recommend as a general rule against using any string that you're going to tune to a higher open pitch than its design pitch. After adjusting for the open-string length, of course (a bass E-string would have the same applied tension if used as an A-string on a 3/4 length neck, roughly speaking). If you do try to tune a string high, it'll have a rather short lifetime. Anecdotally, the lifetime of a cello C-string that I mistakenly mounted as a G-string had a life of less than 30 seconds :-( .
Everyone is so picky about strings and tension and life of their necks. I say just go ahead and give it a try. Guitar necks can take more tension than they are normally subjected to. Everyone told me don't put steel strings on a baritone uke, so I didn't, until one day when I was mad about something, I threw my ukulele across the room. It left a 12 inch dent in the drywall and was completely unharmed. Not even a scratch! I immediately strung it with steel strings and use it like a tenor guitar. That was five years ago and still no neck issues, no fret issues, no tuner issues...it just keeps playing.