It doesn't really matter as long as the approach works for your game. If you don't expect a lot of obstacles in your "playground" a single, large bitmap works just fine.

However, in my 2d RPG, I had to use a tileset for the complicated dungeon-y environments. It made placing things like trees, treasure chests, etc. much easier, because I only had to store it as a value on a tile.

In any case, I think tiling is a neat effect, so that's what I would go with, but you could get away without it.

EDIT:
I'm not sure I answered your question, because I'm not sure what your question is! Did you have any questions more specific than just one-bitmap vs. tile-based?

That all depends on exactly what you're doing.

You could use a single backdrop for your background scenery, but then you can't really do things such as background animations, or interaction between the player and background objects. You'll also be limited to the single background image, and will have to design another one if you want to add some variation.

You could use tiles, and then you can have different tilesets, animated tiles, tile interaction, and tile maps, which will allow you to create various scenes and levels quickly without having to create new graphics.

Or you can go for a single background image and various objects placed on top of it... or a tileset for the background and objects on top of it... or multiple tilesets... and so on. Tilesets are so usefull because they're so generic to handle: every tile is aligned to a defined grid. That doesn't mean placing a sprite and adding a collision shape to your list of objects is a worse method - it depends on the situation.

For example, for a game I'll be working on, we're choosing a layered tilemap approach, so the player can walk behind some tiles and in front of most others. For my own game, I use several tilemaps as well, but I'm adding a sprite-system that allows images to be placed at any location, to hopefully combine the advantages of both: an easy-to handle, natural looking environment. A tilebased approach tends to make levels look square, you see, and that's not something I like too much... ;)

And of course the other advantage of using tiles is that your level will take a fraction of the memory to store than one huge bitmap would, plus checking for collisions with a tile-based map generally requires far less comparisions than running through a list of objects.

I tend to use a combination of a grid-based tile-map for the static background and a std::list or whatever of free-moving objects drawn over the top.