A basic question but there is no such question on Stack Overflow (for ASP.NET)
What I did was pulled the text box in C# code and set it text value to the session. Example:
txtUserName.text = Session["UserName"];
Use it in one of the function which checks the session values or you can use in page_load function (the default function for every page)
Now I think your code should look like <asp:TextBox ID="txtUserName" runat="server" Text='<%# Session["UserName"] %>' >
I always forget the sintax for inline code, this information could be helpfull I think.
I normally hide the implementation details from the aspx code with a property:
.cs file
public string UserName { get { return Session["UserName"]; } }
.aspx
<asp:TextBox ID="txtUserName" runat="server" Text='<%= UserName %>' >