Count shrimp; for each, you need 1/2 slice bacon and 1 soaked wood toothpick.
Arrange bacon slices in single layers in 2 pans, each 10 by 15 inches.
Bake in a 450° oven until bacon begins to brown on the bottom (lift to check), 4 to 8 minutes. As bacon is browned, transfer to towels to drain. Discard fat in pans.
Wrap 1 bacon strip around each shrimp; secure with a toothpick. Spritz the inside of an 11- or 12-inch square hinged grill basket with cooking spray (or lightly brush with oil). Arrange wrapped shrimp in a single layer in basket; close basket. Cook in batches, if needed.
Prepare barbecue for direct heat (see below). When it is medium-hot (you can hold your hand at grill level only 3 to 4 seconds), lay basket on grill and turn as needed to brown bacon lightly, 2 to 3 minutes total. Remove basket from heat, open, and baste bacon-wrapped shrimp with about 1/4 of Mom's barbecue sauce (proportionately less if cooking in batches). Close basket, flip over, open basket, and baste shrimp with another 1/4 of the sauce (less if cooking in batches). Close basket, return to grill, and cook, turning once, until shrimp is opaque but still moist-looking in center of thickest part (cut to test) and bacon is well browned, 2 to 3 minutes longer.
Transfer bacon-wrapped shrimp to a platter. Pour remaining sauce into a bowl. Dip shrimp into sauce to eat.
To prepare grill for direct heat:
If using charcoal briquets, mound and ignite enough briquets to cover the firegrate in a single, solid layer (you'll need about 75). When the briquets are dotted with gray ash, after 15 to 20 minutes, spread them over the firegrate in a single layer. Let them burn down to the desired heat. Set grill in place.
If using a gas barbecue, turn all the burners to high and close the lid for 10 minutes. Adjust the burners to the desired heat.
Notes: Hinged grill baskets are sold at barbecue supply stores; choose one with handles that will fit in your barbecue. You can also use a cooking grate (sold at barbecue supply stores as well) with small holes; watch closely and turn shrimp often to brown evenly. Soak wood toothpicks in water for at least 30 minutes before using to keep them from burning. Buy regular--not thick-sliced--bacon.