Will my record be cleared if I appear for my bench warrant? How?

You should hire a lawyer to go to court to recall the warrant. A lawyer can do this without you present if the underlying charge is a misdemeanor, so it is less risky for you.

Not if you get a conviction.

No. You will have to hire a lawyer to represent you if you want to get the marijuana charge dismissed or reduced to a lesser offense, such as "Littering." If you hire a lawyer, the lawyer can lift your warrant without you having to pay the bond or appear in court (but it depends on which court your case is being prosecuted in and also depends on whether you have a history of multiple warrants.) If you appear in court with an active warrant, they will arrest you and put you in jail. If you can pay the bond, they will usually give you a new court date and release you. If you choose to stay in jail, you will stay until the next time they have court. Then you will go before the judge, who will sentence you if you plead guilty. (Maximum penalty in Missouri for misdemeanor marijuana possession is 1 year in jail and $1,000 fine.) If you plead guilty and do your time in jail, you will end up with a drug conviction on your permanent criminal record, which will prevent you from getting a job, renting an apartment, getting a loan, etc. There is no way to remove a drug conviction from your criminal record, so I highly recommend that you hire an attorney to represent you.

See an attorney, in your case the warrant will disappear but if you do as you were planning a conviction will replace it. A drug conviction is also very problematical during a job searches.

You must first complete your sentence before you are able to expunge your record.