Do you have to be a certain number of feet away from your spouse in order to serve them divorce papers?

No, there is no such requirement.  However, there are several other requirements of which you should be aware in order to give proper legal service .

Usually, your papers must be "personally" served on your spouse or domestic partner. That means that someone, not you, must personally give each of the forms you filed with the court and a blank "Response-Marriage Form" to your spouse.

The server must: be 18 or older; not be involved in your case, and must fill out the "Proof of Service".

They can be: a friend, relative, county sheriff, or process server.

Here is a link to a site that will explain further:  http://www.courtinfo.ca.gov/selfhelp/family/divorce/step2.htm

Note:  If you and your spouse are cooperating on your family law case, and your spouse agrees to accept service by mail, this is the easiest and least expensive way to serve the papers.