var start = MyRichTextBox.Document.ContentStart;
var startPos = start.GetPositionAtOffset(3);
var endPos = start.GetPositionAtOffset(8);
var textRange = new TextRange(startPos,endPos);
textRange.ApplyPropertyValue(TextElement.ForegroundProperty,
    new SolidColorBrush(Colors.Blue));
textRange.ApplyPropertyValue(TextElement.FontWeightProperty,
    FontWeights.Bold);

private static TextPointer GetPoint(TextPointer start, int x)
{
    var ret = start;
    var i = 0;
    while (i < x && ret != null)
    {
        if (ret.GetPointerContext(LogicalDirection.Backward) ==
TextPointerContext.Text ||
            ret.GetPointerContext(LogicalDirection.Backward) ==
TextPointerContext.None)
            i++;
        if (ret.GetPositionAtOffset(1,
LogicalDirection.Forward) == null)
            return ret;
        ret = ret.GetPositionAtOffset(1,
LogicalDirection.Forward);
    }
    return ret;
}

Colorize(item.Offset, item.Text.Length, Colors.Blue);

private void Colorize(int offset, int length, Color color)
{
    var textRange = MyRichTextBox.Selection;
    var start = MyRichTextBox.Document.ContentStart;
    var startPos = GetPoint(start, offset);
    var endPos = GetPoint(start, offset + length);

    textRange.Select(startPos, endPos);
    textRange.ApplyPropertyValue(TextElement.ForegroundProperty,
new SolidColorBrush(color));
    textRange.ApplyPropertyValue(TextElement.FontWeightProperty,
FontWeights.Bold);
}

var textRange = MyRichTextBox.Selection;
var start = MyRichTextBox.Document.ContentStart;
var startPos = start.GetPositionAtOffset(3);
var endPos = start.GetPositionAtOffset(8);
textRange.Select(startPos, endPos);
textRange.ApplyPropertyValue(TextElement.ForegroundProperty, new SolidColorBrush(Colors.Blue));
textRange.ApplyPropertyValue(TextElement.FontWeightProperty, FontWeights.Bold);

private static TextPointer GetPoint(TextPointer start, int x)
{

        var ret = start;
        var i = 0;
        while (ret != null)
        {
            string stringSoFar = new TextRange(ret, ret.GetPositionAtOffset(i, LogicalDirection.Forward)).Text;
            if (stringSoFar.Length == x)
                    break;
            i++;
            if (ret.GetPositionAtOffset(i, LogicalDirection.Forward) == null)
                return ret.GetPositionAtOffset(i-1, LogicalDirection.Forward)

        }
        ret=ret.GetPositionAtOffset(i, LogicalDirection.Forward);
        return ret;
}

<Grid FocusManager.IsFocusScope="True">...</Grid>

private void Colorize(int offset, int length, Color color)
{
    var textRange = MyRichTextBox.Selection;
    var start = MyRichTextBox.Document.ContentStart;
    var startPos = GetPoint(start, offset);
    var endPos = GetPoint(start, offset + length);

    textRange.Select(startPos, endPos);
}

<RichTextBox FocusManager.FocusedElement="{Binding RelativeSource={RelativeSource Self}}">...</RichTextBox>

private static TextPointer GetPositionAtCharOffset(TextPointer start, int numbertOfChars)
{
    var offset = start;
    int i = 0;
    string stringSoFar="";
    while (stringSoFar.Length < numbertOfChars)
    {
        i++;
        TextPointer offsetCandidate = start.GetPositionAtOffset(
                i, LogicalDirection.Forward);

        if (offsetCandidate == null)
            return offset; // ups.. we are to far

        offset = offsetCandidate;
        stringSoFar = new TextRange(start, offset).Text;
    }

    return offset;
}

stringSoFar = stringSoFar.Replace("rn", "")
                         .Replace(" ", "")

var startPos = GetPoint(start, offset);
var endPos = GetPoint(start, offset + length);

var startPos = GetPoint(start, offset);
var endPos = GetPoint(startPos, length);

private static TextRange GetTextRange(TextPointer start, int startIndex, int length)
{
    var rangeStart = GetPositionAtCharOffset(start, startIndex);
    var rangeEnd = GetPositionAtCharOffset(rangeStart, length);
    return new TextRange(rangeStart, rangeEnd);
}

var range = GetTextRange(Document.ContentStart, 3, 8);
range.ApplyPropertyValue(
    TextElement.BackgroundProperty,
    new SolidColorBrush(Colors.Aquamarine));

TextPointer startPos = rtb.Document.ContentStart.GetPositionAtOffset(searchWordIndex, LogicalDirection.Forward);
startPos = startPos.CorrectPosition(searchWord, FindDialog.IsCaseSensitive);
if (startPos != null)
{
    TextPointer endPos = startPos.GetPositionAtOffset(textLength, LogicalDirection.Forward);
    if (endPos != null)
    {
         rtb.Selection.Select(startPos, endPos);
    }
}

public static TextPointer CorrectPosition(this TextPointer position, string word, bool caseSensitive)
{
   TextPointer start = null;
   while (position != null)
   {
       if (position.GetPointerContext(LogicalDirection.Forward) == TextPointerContext.Text)
       {
           string textRun = position.GetTextInRun(LogicalDirection.Forward);

           int indexInRun = textRun.IndexOf(word, caseSensitive ? StringComparison.InvariantCulture : StringComparison.InvariantCultureIgnoreCase);
           if (indexInRun >= 0)
           {
               start = position.GetPositionAtOffset(indexInRun);
               break;
           }
       }

       position = position.GetNextContextPosition(LogicalDirection.Forward);
   }

   return start;
}

private TextPointer GetPoint(TextPointer start, int pos)
    {
        var ret = start;
        int i = 0;
        while (i < pos)
        {
            if (ret.GetPointerContext(LogicalDirection.Forward) ==
    TextPointerContext.Text)
                i++;
            if (ret.GetPositionAtOffset(1, LogicalDirection.Forward) == null)
                return ret;
            ret = ret.GetPositionAtOffset(1, LogicalDirection.Forward);
        }
        return ret;
    }

private void SelectText(int start, int length)
    {
        TextRange textRange = new TextRange(richTextBox.Document.ContentStart, richTextBox.Document.ContentEnd);
        TextPointer pointerStart = textRange.Start.GetPositionAtOffset(start, LogicalDirection.Forward);
        TextPointer pointerEnd = textRange.Start.GetPositionAtOffset(start + length, LogicalDirection.Backward);

        richTextBox.Selection.Select(pointerStart, pointerEnd);
    }