Its possible to emulate a bubble series with the scatter series by changing the marker template to a custom template which binds against a size on on the item.

Width={Binding Item.Size} Height ={Binding Item.Size}

In such a way you could also cause each bubble to have a different color. This doesn't help you with the legend features that you may expect from a bubble chart though, if for example you wanted a size key or a legend item per point in the series.

Here's how you might approach it:
The Xaml:

<UserControl.Resources>
        <DataTemplate x:Key="bubbleTemplate" >
            <Ellipse Stretch="Fill" 
                     HorizontalAlignment="Stretch" 
                     VerticalAlignment="Stretch" 
                     Fill="{Binding ActualItemBrush}" 
                     Stroke="{Binding Series.ActualMarkerOutline}" 
                     StrokeThickness="0.5" 
                     MinWidth="10" MinHeight="10" 
                     Width="{Binding Item.Width}"
                     Height="{Binding Item.Width}"/>
        </DataTemplate>
    </UserControl.Resources>

    <Grid x:Name="LayoutRoot" Background="White">
        <igChart:XamDataChart x:Name="theChart">
            <igChart:XamDataChart.Axes>
                <igChart:NumericXAxis x:Name="xAxis" 
                                      MinimumValue="0" MaximumValue="15"/>
                <igChart:NumericYAxis x:Name="yAxis" 
                                      MinimumValue="0" MaximumValue="15"/>
            </igChart:XamDataChart.Axes>
            
            <igChart:XamDataChart.Series>
                <igChart:ScatterSeries x:Name="scatter"
                                       MarkerTemplate="{StaticResource bubbleTemplate}"
                                       ItemsSource="{Binding}"
                                       XMemberPath="XValue"
                                       YMemberPath="YValue"
                                       XAxis="{Binding ElementName=xAxis}"
                                       YAxis="{Binding ElementName=yAxis}"/>
            </igChart:XamDataChart.Series>
        </igChart:XamDataChart>
    </Grid>

And the code behind:

public partial class MainPage : UserControl
    {
        public MainPage()
        {
            InitializeComponent();

            this.DataContext = new BubbleData();
        }
    }

    public class BubbleData
        : ObservableCollection<BubblePoint>
    {
        public BubbleData()
        {
            this.Add(new BubblePoint() { XValue = 4, YValue = 10, Width = 30 });
            this.Add(new BubblePoint() { XValue = 4, YValue = 4, Width = 40 });
            this.Add(new BubblePoint() { XValue = 8, YValue = 8, Width = 20 });
            this.Add(new BubblePoint() { XValue = 10, YValue = 1, Width = 50 });
            this.Add(new BubblePoint() { XValue = 1, YValue = 10, Width = 40 });
        }
    }

    public class BubblePoint
    {
        public double XValue { get; set; }
        public double YValue { get; set; }
        public double Width { get; set; }
    }

Let me know if this helps!

-Graham