3 inch bleed

Hello All, 

I have a billboard to design, one of my firsts so I'm kinda nervous. Anyways, the billboard size is 10'6''x44' and the printer is asking for a 3 inch bleed all around. He is requesting I design it in 1/4 size so I've broken it down into inches and I came up with 31.5''x132''. I guess I'm looking for a confirmation on my math lol! Anyways how would I achieve the 3 inch bleed all around? Would I design the poster in the measurements I have mentioned or do I actually need to add an additional 3 inches to the layout? I'm not too familiar with the bleed..I ALWAYS seem to have a difficult time doing this. Any help would be greatly appreciated, thank you in advance!!