You're only hope is to contact Remington. They've had to replace a lot of bolts & bolt sleeves on that model so they may be able to help you. I don't guess I have to tell you that the model 710 (and 770 IMO) is possibly the worst epic fail that Remington has ever came out with. If you're fortunate enough to get a bolt fitted to it by Remington I'd strongly suggest selling/trading it off and buy or trade for a better built rifle.
Sorry to hear that. You need to watch Guns - Online Gun Auction - Guns at GunBroker.com for a bolt but it would still have to be fitted. Are you SURE you can't locate the welder and get your bolt back? If you could Remington would fix it for free. Bolt handles breaking off is fairly common for those model 710s. The other thing I've seen is wore out plastic sleeves that the bolt rides in. Perhaps you could buy a bolt where somebody's bolt sleeve bit the dust and they think it's not worth fixing.