Hopefully this sorts all the other downtimes we've been having? Though I won't count on it.
Don't,

.
I'm pretty sure the database errors are due to a backup routine that hogs all the available database connections for an X amount of time. If they actually knew what they were doing, they'd have each database stored twice, once on the live server, and once redundantly. The second one would only be fed data if the primary server could be arsed (in terms of connections and cpu stuffs), so no users would notice it (through database errors).
btw, has someone found out yet whether this is a regular event? I'll go and contact Bluehost tomorrow about this thing, see if they'll send me n00dz of their barely legal and hawt daughters in compensation.