I suppose one huge world map would be a little silly..
You could make a 2D array of image IDs:
DATA 1,2,3,4
DATA 5,6,7,8
DATA 9,10,11,12
for y = 1 to 3
for x = 1 to 4
aGrid(x,y) = read
next x
next y
Then you just keep try of your x,y grid coordinate and then you know which image your character is sat on, which one is above, below, left and right. You can put in control codes like 0 to mean there is no map or it's an unwalkable area.
As for the actual drawing of the background, It looks like people have been suggesting a sliding window type idea, whereby as soon as your character nears a threshold of the screen (like, gets to the right hand third) you scroll the image.
Have a "virtual screen" bitmap - This bitmap will be the one blitted to the screen. I've not touched 2D in darkbasic, but in SDL, you'd copy parts of your source bitmap(s) into a destination bitmap. This way, using the grid method, you can stitch together the background....