When you search for similar items online, try to use a variety of descriptive words or phrases. Sometimes a small change in wordage can get you new results. Attempt to describe what the bowl is made of - metal, wood, glass, porcelain, or pottery. Measure and include the size of the item. Are there handles?
There are other types of small bowls out there including trinket bowls, porridge bowls, covered soup bowls, and bowls for powder or snuff.
Also, include in your search pattern color and patterns. Are there two colors or more? Does the bowl feature flowers, leaves, geometric patterns, fruit, or any other significant details?
Without the name of a company or artist, this may prove difficult, but by trying other descriptions, you may find success.