Hello Isaac,
You can "Save" the text style and the dimension styles, using the "Style > Save" option in the "Text style / Dimension Style" dialog box. The same gets saved in the dgnlib. If you hover over the text / dimension style, it will show you the path of the dgnlib file. You can import these style, using the "Style > Import" and then browse to this dgn/dgnlib file for other project as well. Image below.
Hope this is what you are looking for. If not, please let me know software details you are working with.
