Hi Terri,
Unfortunately, through balloon style is not possible to place part number below slot shape.
It can be achieved by a small automation from VBA code. Before running the code, 2 prerequisites are required.
1. Slot shape defined in a sketched symbol and called it as "SlotSymbol" as shown below.

2. Define a balloon style and called it as "AutoCADStyle". In this, balloon type is set to sketched symbol (SlotSymbol) as shown below. To run the code, balloon name must be "AutoCADStyle".

After creating sketched symbol and balloon style, run the following sample VBA code.
Sub main()
Dim oDrawDoc As DrawingDocument
Set oDrawDoc = ThisApplication.ActiveDocument
Dim oBalloon As Balloon
Set oBalloon = ThisApplication.CommandManager.Pick(SelectionFilterEnum.kDrawingBalloonFilter, "Select a balloon")
Dim oStyle As BalloonStyle
Set oStyle = oDrawDoc.StylesManager.BalloonStyles.Item("AutoCADStyle")
oStyle.Properties = "FormatID='{32853F0F-3444-11d1-9E93-0060B03C1CA6}'PropertyID='5'"
oBalloon.Style = oStyle
Dim s As String
s = oBalloon.BalloonValueSets.Item(1).Value
oStyle.Properties = "PartsListProperty='45572'"
oBalloon.Style = oStyle
Dim txtPt As Point2d
Set txtPt = ThisApplication.TransientGeometry.CreatePoint2d(oBalloon.Position.X, oBalloon.Position.Y)
txtPt.X = txtPt.X
txtPt.Y = txtPt.Y - oBalloon.Style.BalloonDiameter
Dim oText As Inventor.GeneralNote
Set oText = oDrawDoc.Sheets.Item(1).DrawingNotes.GeneralNotes.AddFitted(txtPt, s)
Set txtPt = ThisApplication.TransientGeometry.CreatePoint2d(oText.Position.X, oText.Position.Y)
Dim wide As Double
wide = oText.Width
txtPt.X = txtPt.X - (wide / 2)
oText.Position = txtPt
End Sub
On running the code, a prompt will appear to select a balloon. After successful balloon selection, a text will be created below slot shape. Text contains respective part number of the selected balloon.
Please feel free to contact if there is any doubt.
If solves your problem, click on "Accept as solution" or give a "Kudo".
Thanks and regards,
CHANDRA SHEKAR G
Developer Advocate
Autodesk Developer Network