This should do it, it applies a filter to the data and leaves only rows showing that are "blank" in column B. Then it deletes all visible rows.

Option Explicit

Sub RemoveBlanksInColB()
Dim LR As Long

Application.ScreenUpdating = False
With ActiveSheet
    .AutoFilterMode = False
    .Range("A1:A9").EntireRow.Delete xlShiftUp
    .Rows(1).AutoFilter 2, "="
    LR = .Range("A" & .Rows.Count).End(xlUp).Row
    If LR > 1 Then Range("A2:A" & LR).EntireRow.Delete xlShiftUp
    .AutoFilterMode = False
    .Columns.AutoFit
End With
Application.ScreenUpdating = True
End Sub