If you are able to modify the FullBucket class, I would add a MinDays (int) property - and change the Linq/SQL to return a value for it.
If you are not able to modify it, can you derive a sub-class that expresses a MinDays property? In the sub-class, MinDays would be a get-only property, whose get expression is something like the following:
public int MinDays
{
get
{
var minDaysText= (Type == null ? "" : Regex.Match(Type, "^[0-9]+").Value);
minDaysText = string.IsNullOrEmpty(md) ? "99999" : minDaysText;
return int.Parse(md);
}
}
And, if you will be using MinDays regularly, you should add a nullable private field (int?), and set its value on the first reference ... so you don't have to do the regex on every reference.