Bush attracts Flies & they sneak in house 4 dinner!

Please help me. I just moved and have a Bush outside of my new home that attracts every type of fly bee etc. It doesn't smell too bad and I am told by prior owner it retains the leaves in winter and does not flower but has little yellow buddy dots that look like they should flower. I am tired of chasing flies. Everytime I open the door they come in and then hang out while I am cooking dinner. I was supposed to be brining some great cucs right now but I was getting rid of 5 flies after opening the door. Can anyone tell me what this bush or shrub is? It stands about 5 feet high. I can take a pic and send it. It looks preety and I really do not want to hurt it and cut it down there must be an answer.
Thank you so much I really appreciate any response.
Smiling not too wide might catch a fly:)

Please post a picture, and what area you live in.