Ellipsis with a period/fullstop

From the MLA Handbook for Writers of Research Papers, Seventh Edition, section 3.7.5. "Ellipsis":

For an ellipsis within a sentence, use three periods with a space before each and a space after the last ( . . . ).

As an example it shows:

Quotation Omitting a Sentence

In discussing the historical relation between politics and the press, William L. Rivers notes:

Presidential control reached its zenith under Andrew Jackson, the extent of whose attention to the press even before he became a candidate is suggested by the fact that he subscribed to twenty newspapers. . . . For a time, the United States Telegraph and the Washington Globe were almost equally favored as party organs, and there were fifty-seven journalists on the government payroll. (7)

So there are no [] or (). For my MLA papers, I have a macro for the "quotation-ellipsis":

\usepackage{xspace}
\newcommand{\el}{{\,\ldots}\xspace}

The small space \, takes care of some weird spacing in \ldots, that seemed to look best to me. \xspace makes sure it works as bla bla \el. and as bla \el bla., i.e. a space is added only if there's no punctuation after the macro. The ellipsis package might be even better for this purpose, but I've never really looked into it since this solution worked for me.

This might just be personal preference on how you specify the spacing. Consequently, this is just one suggestion. Others may have, well, other suggestions.

You could force the space around the ellipsis using a command space \ :

``This is a book.\ldots That is my bag''
``This is a book. \ldots That is my bag''
``This is a book. \ldots\ That is my bag''
``This is a book.\ \ldots\ That is my bag''

See What does \  exactly do? for a discussion on using command space \ .

The answer probably depends on the publication's style guide.

Note, too, that the exact spacing may be altered by other factors (e.g. \frenchspacing).

The ellipsis package documentation (texdoc ellipsis) discusses the issues around this in some detail and the package provides options to satisfy the aesthetes and the style guides -- though not always both at the same time.