If you wanted to describe the sound of a small brass bell that you can hold in your hand (this is an example image of what I mean - what word would you use? Brrring? Bling?
The term should be tinkle. For example:
- A bell tinkled as the door opened.
- The maid tinkled a bell.
The sound of a hand held brass bell, to me, is "ding-a-ling."
"Tinkle" would apply at best to a very small bell (and at worst is slang for urinate as I commented above), and "brrring" would apply to the repeated hammering on a bell such as one used to hear telephones or school bells make. "Bling" is slang for gaudy jewellery!
Edgar Allen Poe's poem The Bells pretty much covers this. In this poem:
sleigh bells tinkle and jingle,
wedding bells ring and chime,
alarm bells clang,
funeral bells toll and knell.
For small bells, I think tinkle, jingle, ring would all apply.
The sound of a small brass bell is a ‘tintinnabulation’.