It very much depends what the existing plumbing looks like. If the existing sewer line is below the basement slab, then it's a matter of breaking up the slab and connecting to the existing line. Since sewer lines drain by gravity, the position of the bathroom will likely be predicated by location of the existing sewer line. The other option is to install a pit and use an ejector pump.

Remember that any time you turn basement space into sleeping space, you need to worry about egress. So you'll need to check with your local code enforcement folks about their requirements.

As for cost, it's impossible to say without knowing a lot more about your home and where it is located but bathrooms add a lot to the cost of a basement remodel.