One problem with this explanation is that it flatly contradicts the timeline in Luke 24, especially:
"Now on the first day of the week, very early in the morning, they, and certain other women with them, came to the tomb bringing the spices which they had prepared. ... He is not here, but is risen! Remember how He spoke to you when He was still in Galilee, saying, 'The Son of Man must be delivered into the hands of sinful men, and be crucified, and the third day rise again.' And they remembered His words. ... But we were hoping that it was He who was going to redeem Israel. Indeed, besides all this, today is the third day since these things happened." (vv. 1,6,7,8,21)
Jesus interprets this usage for us infallibly when He said, "Behold, I cast out demons and perform cures today and tomorrow, and the third day I shall be perfected." (Luke 13:32)
So it would be impossible for Jesus to be crucified in any day other than Friday and to have thee things fulfilled "on the third day" which we know was Sunday. Bullinger just got it plain wrong in his Companion Bible.
Another problem is that this explanation does not seem to square with what earlier Jewish writers taught on the subject, e.g.,:
A day and night are an Onah [‘a portion of time’] and the portion of an Onah is as the whole of it." (from The Jerusalem Talmud: Shabbath ix as quoted in Hoehner, Harold W, “Chronological Aspects of the Life of Christ—Part IV: The Day of Christ’s Crucifixion,” Bibliotheca Sacra).So any portion of a day fits within the designation "a day and a night". So then three days and three nights do not have to fit neatly into a fixed 72 hours time slot.
Another author put it this way:
The principle which governed their [Jewish] thinking in such matters has been rather clearly set forth in some of their own commentaries on the Scriptures. It is this: that any part of a whole period of time may be counted as though it were the whole. A part of a day may be counted as a whole day, a part of a year as a whole year. Furthermore, a part of a day or a part of a night may be counted as a whole "night and day." I suspect that in the Lord's parable of the man who paid his labourers for a whole day, whether they had worked for a whole day or not (Matthew 20:1-16), is really a reflection of this principle. Thus, in the Babylonian Talmud, the Third Tractate of the Mishnah (which is designated "B. Pesachim," at page 4a) it is stated: "The portion of a day is as the whole of it." (Arthur Custance)
Dan 7:25 And he shall speak great words against the most High, and shall wear out the saints of the most High, and think to change times and laws: and they shall be given into his hand until a time and times and the dividing of time.