But Neisseria is going to be always smaller than the cells, even if the bacteria is been phagosized, you could be able to identify them within the cytoplasm of the macrophages or phagocytes; so, even if they are outside the cells, in the interstitium of the tissue, you will be able to seen them.

Mind the magnification you use in your microscope (though they are usually limited to 100X or 120X) or try to scan the slide, whereby you will be able to acces all kind of magnification we are unable to see with a common microscope.

You should better define what you HAVE done already and what you are going to try...., i.e.:  

i)you have ? cultured endometrial adenocarcinoma cell lines HEC1B and/ or  human endometrial/uterus cells /sections of the latter? 

Re: sections: either cryosections of cultured cells or sections from paraffin embedded culture?, or would you like to stain the cultured cells intravitally in the wells.....?

Furthermore:

ii) application of a "classical" histochemical stain (dye, staining method,Gram stain)

iiia) application of IHC or ICC

iiib) application of a specific FLUOR-staining (if available).

Of interest also would be a short explanation WHY your (epithelial) cells harboring or surrounded by / with  the gram negative bacteria shouldn't be stained....It would be of help to answer your question....

NB: edited 1 min after saving the original/first answer:   regarding

iv) what is the purpose of staining only the bacteria (i.e. only localization - distribution of N. g. , morphology

regarding:

i) e. g: cf. https://www.microbiologyinpictures.com/bacteria-photos/neisseria-gonorrhoeae-photos/neisseria-gonorrhoeae-gram.html  or also

 cf. e.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2095009/   find specific text in section: 'Presumptive identification of N gonorrhoeae'

or https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1045783/ [Methyl green-pyronin (MGP)] with recipe. or also:

http://vlab.amrita.edu/?sub=3&brch=73&sim=208&cnt=2   (smears) and 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC175593/pdf/654122.pdf  (application of Wright's stain to cultured cells) or

http://onlinelibrary.wiley.com/doi/10.1002/mbo3.432/pdf  (Silver staining) 

for i) and ii) cf.: http://link.springer.com/protocol/10.1385/0-89603-535-2%3A15#page-2   section 1.3.:   "Standard diagnostic methods"

for iiia) http://link.springer.com/protocol/10.1385/0-89603-535-2%3A15#page-2 cf :  1.3.2: Antigen detection.

for iiib)  cf. e.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2095009/   find specific text in section "Serology tests" . 

@ http://www.aafp.org/afp/2006/0515/p1779.html: 

"Two methods for detecting N. gonorrhoeae are culture and nonculture tests. Culture techniques are considered the tests of choice; but nonculture techniques, which are less labor-intensive and are similar in accuracy to cultures, have replaced culture techniques in some instances. The newest nonculture technique is the nucleic acid amplification test. This test has good sensitivity (92 to 96 percent) and specificity (94 to 99 percent) compared with cultures.1 "

For more results: search Google and/or Google Scholar  e. g. for  | Stain* Localization  "Neisseria gon*" | 

Best wishes and good luck

If you have a confocal microscope you could just perform FISH with a fluorescent Neisseria specific probe after Amann et al., 1991. Or just start with the universal bacterial probe Eub_338. In this case you will detect all bacteria present in the cell culture. 

The procedure is rather simple and not time consuming. Fix cells with 4% PFA in PBS for about 20-30 min on Superfrost slides to ensure cell attachment, wash with PBS to remove the fixative, postfix with a drop of methanol. Wash again with PBS. Avoid drying the slide to reduce background fluorescence. then add the probe in Hybridization buffer, cover with a piece of parafilm and hybridize in a wet chamber for 1.5 h at 46 C. Then wash twice with washing buffer without covering with parafilm for 30' each wash at 48C. Mount in Mowiol and cover with a coverslip. The epithelial cells will not be stained, the bacteria should give a clear signal in the confocal.

Have a try!