Critique Circle does not support submitting stories directly from your word processor or with any formatting unless you export it first as HTML which you might not want to do as that will not allow you to receive inline critiques.
There is a way to convert some of the most used formatting from MS Word to CC-compliant text.
CC supports bold, italics, underline and centered text, and you can convert such text in MS Word to CC formatted text before copy/pasting your text into CC's "Submit Story" window.
To do that open up your find-replace option in MS Word (Control-H), make sure you are working in a throwaway copy of your manuscript so that you don't accidentally save over it though.
In the find-replace dialog make sure you have your focus in the "Find What" text box (just click it) and then click on the "More" button, at the bottom of the dialog there is a "Format" drop-down button. Click that and select "Font". Now, select "Font Style">"Bold" and click ok.
NOTE: There is an easier way 
You can press control-b to toggle bold, control-i to toggle italics, control-u to toggle underline and control-e to toggle centered. Just remember to have your focus on the "Find what" box and clear out previous formatting before entering a new one (f.ex. it might say "Not Bold", which is not the same as not searching for bold text. In this case you should hit control-b again to clear the bold flag)
Under the "Find What" text box you should now see "Format: Font: Bold".
In the "Replace With" text box, enter [ b ]^&[ /b ] (without the spaces) and click "Replace All".
This will find every piece of Bold formatted text and encase it with [ b ] and [ /b ].
Do the same with italics, underline and center (that's in the "paragraph" option group). In every case, make sure that the option you had before is no longer selected, so that only bold, italics or centered is shown below the "Find What" text box.
Even if you have text that is italics _and_ bold you use the same method.
Here are the codes you want to put into "Replace With":
Bold: [ b ]^&[ /b ]
Italics: [ i ]^&[ /i ]
Underline: [ u ]^&[ /u ]
Centered: [ c ]^&[ /c ]
Remember to omit the spaces when you write these in.
Now that you've done these four changes you can copy the text from your manuscript into CC's "Submit Story" window and voila, you've got (some) formatting
Note: Although this applies to Microsoft Word you are sure to find similar tricks for other word processors.