string str="abcaaa <begin> A111b0basd123aaa <end> abcaaa <begin> A1161bbasd123aaa <end> aaaddd <begin> A1311bbbasd123aaa <end>";
System.Text.RegularExpressions.Regex  reg=new  System.Text.RegularExpressions.Regex(@"(?<=<begin>\s+)(?<Linkurl>[^><](\w+)?bbb(\w+)?)(?=\s+<end>)",System.Text.RegularExpressions.RegexOptions.IgnoreCase);  
System.Text.RegularExpressions.MatchCollection m = reg.Matches(str); //设定要查找的字符串
for (int i = 0; i < m.Count; i++)
{
    Response.Write(m[i].Groups["Linkurl"].ToString()+"<br>");
}

string str="abcaaa <begin> A111b0basd123aaa <end> abcaaa <begin> A1161bbasd123aaa <end> aaaddd <begin> A1311bbbasd123aaa <end>";
System.Text.RegularExpressions.Regex  reg=new  System.Text.RegularExpressions.Regex(@"(?<=<begin>(\s+)?)(?<Linkurl>[^><](\w+)?bbb(\w+)?)(?=(\s+)?<end>)",System.Text.RegularExpressions.RegexOptions.IgnoreCase);  
System.Text.RegularExpressions.MatchCollection m = reg.Matches(str); //设定要查找的字符串
for (int i = 0; i < m.Count; i++)
{
    Response.Write(m[i].Groups["Linkurl"].ToString()+"<br>");
}

<begin>[^<>]*?bbb[^<>]*?<end>