Unfortunately, AI still offers no support for in-line graphics. So the simple (in other illustration programs) matter of using a native graphic as a bullet inside text is not an option.
So, set up a hanging indent Paragraph Style for the bulleted paragraphs and a Character Style for the dingbats:
In Character Map (or AI's Glyphs Palette), peruse a dingbat font for a glyph which you want to use as the bullet. Note what the keyboard character is for that glyph.
Back in AI, in an AreaType object, type:
The character corresponding to the desired dingbat glyph
The text of the first bullet paragraph
Open the Tabs window and set tabs for a hanging indent, something like:
Left margin: .5"
First line indent: -.5"
Centered tab at .25"
Left tab at .25"
From the Paragraph Styles flyout menu select New Paragraph Style. Name the new style "DingbatLine". Click DingbatLine in the styles list to apply it to the current paragraph.
Select just the character you typed in place of the desired dingbat. Change its font to the dingbat font. From the Character Syles flyout menu select New Character Style. Name the new style "Dingbat". Click Dingbat in the styles list to apply it to the current character.
Thereafter, while typing the text, key:
The character corresponding to the dingbat glyph
The paragraph text
Apply the paragraph style to the paragraph. Then select the dingbat character and click the Dingbat style in the Character Styles Palette.
Beware of a bug in AI relating to text Styles: If you later scale the whole AreaText object, its tab spacings will not scale accordingly. So be sure to create your styles at the actual text object size you desire.