Sewer smell coming from my bathroom sink!

You may have a blockage in the exhaust pipe on your roof. I don't know the actual name if it but the hubs refers to it as the 'stink pipe'. It lets out any gasses from the toilet and sink to the septic. I'd call a plumber.

It may be sewer gas. That happens when a drain isn't used enough to keep water in the trap. If it is allowed to dry up, it lets in sewer gas and comes up the empty pipe. Run water in all the sinks and stand alone drains that don't get used enough. You can clean the pipes surrounding the sink drains by using baking powder, followed by vinegar, let them fizz for a while and follow with boiling water to flush all the gunk out, just in case that is where the smell is coming from. You can do the same with your shower drain, you never know if the gunk in the drains is the culprit or not. I hope this helps! Good luck!

If there wasn't any leaking indicating that the p-trap might not be sealing correctly, check and clean out any hair/gunk from the drain. Try putting about 1/4 cup baking soda in the drain, then 1 cup of white vinegar. Let it sit in there for about an hour and then pour several gallons of almost boiling water down the drain.

bleach poured down the drain

You may have a deeper problem than you should deal with on your own. If you have a septic tank I would look into getting that pumped out asap.

You did things right so far. The p trap holds water to prevent sewer gas from migrating into the room. Next step would be to check the vent pipe on the roof and see if it's clogged. Leaves, birds, and varmints can fall into it and clog it. If it is, anytime the toilet or shower is used it sucks the water out of the sink p trap. A toilet flush can also gurgle. Use a garden hose at full blast and try to flush.force the clog down through the roof vent. If water starts backing up it will need to be rodded through.