This sounds like a civil case (assuming you borrowed money from your friend and there is an issue of repayment) in which case if you comply with any order the Court issues, this will not go on your criminal record.
But wait! I am concerned that you are thinking of not going to your hearing. You should contact the court to make arrangements to reschedule the hearing to a date when you are available to attend. If you simply don't show up, the Judge most likely will issue a judgment against you. Sending a letter to the Court might not make it to the right file in time, and is not likely to be admissible under the rules of evidence. Bottom line: either go to court, get the hearing date rescheduled, or find a way to repay your friend and have her withdraw the case.
It sounds like you want to make a payment plan to repay your friend. You can contact your friend to make a settlement offer. Just make sure that you pay in a way that leaves you with proof that you paid. Either pay by check - so you have the returned check - or get a receipt from your friend for any payments you make in cash (not preferred).
BTW, if you do end up in front of the Judge, you should bring as much documentation as possible to prove that you don't have the funds to pay back the debt (i.e. bring a bank statement showing your balance, documentation of your obligations, etc.) Don't expect to have another chance to come back with proof.
If you cannot be present at trial, you should attempt to have the trial continued to another date. Better yet, if you admit that you owe the money, why not attempt to work out a payment plan with your friend. If you can do that, you avoid a judgment against you and judgment interest. A civil judgment does not get reported on your criminal record, because it is not a crime.
Civil matters do not go on your criminal record. This civil matter may become a criminal matter, however, if your ex-friend later claims that you stole this money from her. If that happens, you'll receive a summons to appear for a clerk's hearing to decide if there is probable cause to issue a complaint against you. For the time being, I would suggest that you file a motion to continue the trial, stating the reasons you need a continuance, and then work out a repayment plan at your next court date. Good luck.
Assuming this is a civil matter at this stage, you should make very effort to appear in court, or notify the clerk that you are unable to appear or send someone to stand in for you and request that the court continue (postpone) the matter. Be prepared to provide several alternate dates when you are available.
If you acknowwledge the debt, you can let the court know that you intend to pay it and that you will do so over time.