high risk of preterm labor

I don't know if it makes a difference in your ammount of worry, but many women with bicornate uteri go on to have healthy term babies. There is at least one story of such in Spiritual Midwifery by Ina May Gaskin- maybe reading it will calm some fears.
You can do some things that every pregnant woman can do to lower her risk of preterm delivery- eating right withplenty of protein, and calcium-magnesium, and water are excellent routes for all pregnant woman bicornate or not.

Good luck! Value the baby you have within you as a full fledged child- with any luck you will meet him or her within two or three weeks of your due date.

My sister has a bicornate (heart shaped) uterus and just delivered her 2nd baby last week - a healthy, 8 1/2 pound boy, born 9 days "late"! Her first baby, now 2 years old, was delivered by c-section - because she was breech and was tangled in the umbilical cord. The midwife said that the first baby was "stuck" in the dip in her uterus and could not turn. Same with the second baby - but during an US 2 weeks before her due date - surprise - the baby had turned and was head down. She delivered him VBAC. Smooth labor - no complications - no pain meds!
The risk of preterm delivery was not mentioned to her by her midwife... so this wasn't a concern for her - just the position of the baby.
I hope that these "success stories" help put you at ease.
Congratulations!