I saw something brownish-grey that looked like a ball that dashed by me and scared the **** out of me.

Was that a roach or a mouse?

I live in an apartment and I cleaned up a little...does that mean I may face more bugs and mice?

Sounds like a mouse, Contact your landlord asap about it.

Buy yourself a few of these:

http://www.amazon.com/Smart-Mouse-Trap-Humane-Mousetrap/dp/B000YFA7HW

I have had a few mouse problems in my apartment over the years and have tried every trap. This one works time after time.

i have 6 cats and I STILL had to go buy one of those glue traps to catch our mouse, he just crawled right on there and went to sleep.

Assuming you don't have any pets here's something that's worked for me:

I bought PURE peppermint oil (NOT peppermint extract) & a cheap spray bottle. I got the peppermint oil at Whole Foods but anyplace that sells pure oils will do. Put about 70-100 drops in the spray bottle with 12 oz of water and spray around your baseboards. Mice tend to scurry against walls bec. they have very poor sight. You should repeat this every day. In about 5 days or a week you should stop seeing mice/evidence of mice. I will warn you your apartment will smell like a candy cane factory but since I like the smell of peppermit it didn't bother me personally. Also - avoid getting any of the oil on you - it may irritate your skin - the oil is very potent - and do not use it in any food - it is probably several hundreds time more concentrated than the peppermint extract you can buy in the supermarket. Basically what happens is that peppermint oil is to mice what ammonia is to our noses. Mice (also rats) HATE the smell of it and will relocate elsewhere far away.

Make sure anything in a cardbooard container is in a cabinet (and of course check your food cabinets to make sure no mice have been there)

^That is good advice. If there are holes or cracks anywhere in your apartment try plugging them with steel wool.

I'm also getting small grey and brown roaches in my bathroom.

Are those Water Roaches (American Roaches) or Nazi Roaches (German Roaches)?

Also...I see those roaches once or twice a week.

yes these are all bugs,i know they all really disturbing and make lots of mess in my bathroom....they irrated me for about 1 month