Lions boss Woodward announced the largest squad in Lions history on Monday, but Scotland captain Bulloch will make the journey to the southern hemisphere with Chris Cusiter and Simon Taylor his only compatriots.
Full-back Chris Paterson and flanker Jason White are the surprise omissions from a 44-man party which includes 20 Englishmen.
But Glasgow hooker Bulloch believes the fact that Scotland only just avoided a wooden spoon in the Six Nations is behind Woodward's decision to turn his back on players north of the border.
He said: "It boils down to the fact we only won one game against Italy, and even then we didn't win it convincingly.
"I think Clive has said that he wants to take winners and in the last two seasons Scotland have not won as many games as we would have liked.
"That's going to count against us in terms of selection.
"I'm gutted for the guys that didn't make it, I would have put my mortgage on Jason White being in the squad along with Tom Smith and Chris Paterson.
"I'm just delighted to hear I'm in the squad.
"It's obviously been tricky, we (Scotland) have not had our worries to seek, so to get on this tour was one of my goals at the start of the year."
Bulloch was taking nothing for granted ahead of the squad announcement after thinking he had done enough to merit a place in the Lions' tour of Australia in 2001.
The 30-year-old was not named in the original squad for the trip Down Under but was later called up as cover.
He added: "It's great, obviously I went through the whole waiting process last time and that didn't happen, and over the weekend I thought I had a 50/50 chance of making it.
"The last time it was pretty difficult because the guys had some time together back home. They went through a lot of bonding exercises in England and it was quite difficult to jump straight into a tour.
"To be selected this time is a great achievement, I can go out there now and prepare for it properly."