In the alliterative poem, Death and Liffe from the Percy Folio MS. [?] copied many places, there are three instances of the word “beliue:”

& the grasse that was gray greened beliue. --line 73

then thou hyed into hell hole, to hyde thee beliue ; --line 387

what with wandering & with woe I waked beliue. --line 452

--Death and Liffe: an alliterative poem, by James Holly Hanford and John Marcellus Steadman, Jr., USC, Chapel Hill, 1918 [link_01(GUI)]—link_02(djvu.txt)]

From the index in the above linked work, I see that “beliue” means “quickly.”

Initially, I was unable to discover an etymological resource citing “beliue” online.  I suspected that it was related to “be live” or “believe” but that turned out to be incorrect--at least I could not easily find any obvious connection.  Then I discovered the Taill of Rauf Coilyear.  Therein, I found six instances of “beliue” in the text and a definition bearing some etymological significance in the “Glossarial Index”, on page 155 in the applet (or numbered page 126 in the actual work):

(from the “Glossarial Index” pages mentioned above)

Beliue, 6/94, adv. quickly, at once. O.E. bi life == with life

I am curious, am I on the right track thinking ”bi” or ”bis” as in twice? 

As in “again alive,” or “twice as much alive,” or “even more alive” for the above quoted “with life?”

Is there a handy online Old English [and/or Middle English] resource that I am not finding?

I am curious, am I on the right track thinking ”bi” or ”bis” as in twice? 

No, it’s just the OE form of the preposition by.

Blive or biliue (and other variants) is a rather common Middle English adverb meaning “quickly, vigorously.” It is indeed from the phrasal bi live, “with life/vigor.”

Here’s the MED entry. The MED is usually the best source for Middle English words. For the period, it’s much more comprehensive than the OED.

Thanks, Dave.  That is a truly excellent resource. 

I don’t know how I missed it.  It’s on the wordorigins resource page and also enjoys a thread of its own.

I am curious, am I on the right track thinking ”bi” or ”bis” as in twice? 

No, it’s just the OE form of the preposition by.

As in “betimes” = early?

and perhaps in terms which we still use, e.g. “below”, “beneath”, “behind”?

That’s right.

Also interesting that the word “quick” also means alive—as in cut to the quick.  So the modern word shares either an origin or a connotation with the OE word.

But the connection may just result from translators’ choice.