You can clean narrow-neck bottles, even ones that are a weird shape - like my hummingbird feeder - for free, without a brush.
Step 1: Tools
A bottle that needs cleaning.
Step 2: A Spoonful of Rice
Just a plain teaspoon full should do. You can add more if it's a big bottle, but it doesn't take a lot. Don't put it in yet.
Step 3: A Squirt of Soap
Any kind of dish soap is okay. You don't need to add much, just enough to "glue" the rice together on the spoon. (About half a teaspoon here.) You don't need to mix it in.
Step 4: Slide It In
Tip the contents of the spoon slowly into the bottle. The soap acts as "glue" so the rice doesn't spill all over your kitchen.
Step 5: Add Water
Fill up the bottle about halfway with water (more than in this pic)
Step 6: Swirl and Rotate
Cap the open end with your finger and gently shake, rotate, and invert the bottle, so the rice grains come in contact with the glass.
Step 7: Rinse
Empty the bottle and give it a really good rinse, to get all the soap out. Ta da!
(If you're doing this for a hummingbird feeder, you can also give it a rinse in a mild bleach solution before the final rinse.)