I'm storing some textual data into database which cannot contain HTML tags. For line breaks, I'm using \r\n and the output is fine when I view it in a tool known as Service Cloud (FKA RightNow)
Similarly, is there a way in which I can bold a part of text using a similar technique as \r\n?
Where are you storing this text? If this is a field that supports rich text, like standard text, then you can bold the text through rich text encoding. However, you're likely working with a generic text (ASCII characters) field, which does not have formatting. If that's the case, then no, you cannot format it.