You restore important data from backups.
The problem with "Ten Things To Do To Secure An Important Persons Computer" is that it forgets the usual definition of Information Security:
protecting the confidentiality, integrity and availability of information
I guess this isn't really an answer. However, I hope it will nevertheless be helpful to others.
Sadly, I think you've learned a rather harsh lesson regarding the use of encrypted drives, especially removable ones.
All encrypted drives whether removable or not are more sensitive to corruption issues. This makes it even more important to ensure that you have the data backed up. Clearly, the backup also needs to be encrypted and again this means that you should keep several copies of backups. The realistic minimum for backups is THREE. These should be kept in different locations.
For home use, I keep data on local PC's, copied on the NAS (the NAS drive data is duplicated within the NAS, not really a robust backup but convenient if a local disk fails) and copied to a secure cloud backup such as CrashPlan.
No form of removable media can be considered robust. Flash based memory sticks are as liable to faile as any other removable media. I don't know what the exact stats are but my own experience is that a memory stick is just as likely to fail as a hard drive, rather less than an old-fashioned floppy disk. CD's and DVD's are very variable in their reliability with some failing after a couple of years of storage, others lasting a decade or more.
Sorry about the lack of a real answer but I think this is always worth repeating so that more people understand the need for good backup processes.
Best Answer
Yes you can still continue to work while BitLocker encrypts in the background.