Yes you can trademark a Bumper Sticker.
If you are using a particular word, graphic, phrase or slogan on a Bumper Sticker, you can trademark it to prevent any other Bumper Sticker manufacturers from using it without your permission. For example, see the mark “Salt Life” to see a registered trademark for a Bumper Sticker. A Bumper Sticker trademark entitles the owner of the trademark to stop others from using their mark or a similar mark on a Bumper Sticker without their permission. Other types is bumper stickers, plastic film, decals, stickers, and magnetic.
To trademark a Bumper Sticker, the word, graphic, phrase or slogan must be non-descriptive and unique to merit trademark protection. The United States Patent and Trademark Office will reject your trademark application if they determine that your word, graphic, phrase or slogan is too similar to a prior registered trademark.
By Mat Grell, US Trademark Attorney