I have gone through the links courses I have played in GB&I, and come up with these bunkerless holes.
1 St. Enodoc, Carne, Portsalon, Portstewart, Valley, Bushfoot. Brora, Burnham and Berrow, Channel
2 Perranporth, Enniscrone, Bushfoot, Channel
3 St. Enodoc, Saunton East, Carne, Enniscrone, County Louth, Channel
4 Tenby, Dunfanaghy, Rosses Point, Enniscrone, Valley, County Louth, Fortrose and Rosemarkie, Bernham and Berrow
5 Perranporth, Dunganaghy, Portstewart, Valley, Fortrose and Rosemarkie, Channel
6 Saunton East?, Carne, Portsalon, Rosapenna OT, Dunfanaghy, Dunluce, Valley, New
7 Perranporth, Saunton West, Carne, Narin and Portnoo, Dunfanaghy, Donegal, Portstewart, Valley, Tarbat, Golspie, Channel
8 Saunton East?, Dunfanaghy, Castlerock, Valley, Jubilee, Channel
9 Perranporth, Castlerock, Tarbat, New, Channel (Does it count? It has a grass bunker!)
10 St. Enodoc, Perranporth, Narin and Portnoo, Castlerock, Dunluce, The Castle, Jubilee, Narin and Portnoo
11 North West, Dunfanaghy, Enniscrone
12 Bude and North Cornwall, Perranporth, Carne, Dunfanaghy, Enniscrone, Burnham and Berrow
13 Perranporth
14 Perranporth Braid's Best, Carne, Enniscrone, County Louth, Royal Dornoch, The Castle, Eden, Burnham and Berrow
15 Enniscrone
16 Bude and North Cornwall, Portsalon, Enniscrone, Dunluce
17 Bude and North Cornwall, Narin and Portnoo, County Sligo, Enniscrone, Portstewart
18 Perranporth, Carne
Some preliminary observations. By the time you get to the seventh hole you can relax and not build a bunker. By the time you get to the 15th hole, you had better build a bunker, or have a terrible logo.
If you are in Fife, there are so many flush golfers around you can build as many bunkers as you would like.
I will try to pick some to make my eclectic 18, but if I leave some out, i may need some help from other posters.
EDIT: I went ahead and picked the rest since no one offered any input. :TIDE
As I have engaged in the infamous hit and run on a tight schedule, thereby having trouble recalling much about many of these holes. For example, I was so intent on downing Bill Thomas in our singles match at Enniscrone, my recollection of the course is primarily long walks green to tee in hollows on the holes in the dunes, and several somewhat flat holes outside the dunes. However, the flyovers on their website made me realize I think I would like the place much more if I were to give it another go. Enniscrone will make my list as they are the only course to have the cajones to have no bunkers on the 15th hole.
1. Brora 4
2. Perranporth 5
3. Enniscrone 3
4. Tenby 4
5.
Fortrose and Rosemarkie 4 The hole i intended to use was the 4th. Placed it at 5 by mistake. Have to find an altenative.
5. Portstewart Strand 4
6. Portsalon 4
7. Tarbat, the new longer version 3
8.
Dunfanaghy 4, I forgot I played at Burnham and Berrow. My favorite 8th hole is now the eighth on the Channel course. This may require quite a bit of reshuffling if I choose the Channel hole.
8. Portrush Valley 5
9. Castlerock 3
Front nine par
34 35
10. St. Enodoc
5 4 I was confident this was a par 5 when I played it. Learned from Sean's 18 that it is now a 4. More reshuffling needed.
11. Narin and Portnoo 5 Since Hanse dropped a par 3 earlier in the course, this hole turns out to be #10, so more adjustment necessary.
11. North West 4
12. Bude and North Cornwall 4
13. Perranporth 4
14. Royal Dornoch 4
15. Enniscrone 4
16. Dunluce 3
17. County Sligo 4
18. Carne 5
Back nine par
38 37 36