public class ConfigurationProvider : Provider<Configuration> {
    public class ConfigurationProvider(string connectionString
        , Assembly mappings) {
        ConnectionString = connectionString;
        Mappings = mappings;
    }

    protected override Configuration CreateInstance(IContext context) {
        var c = new Configuration().Configure();
        c.AddAssembly(Mappings);
        c.Properties["connection.connection_string"] = ConnectionString;
        return c;
    }

    private readonly string ConnectionString;
    private readonly Assembly Mappings;
}

public class ConfigurationService {
    public ConfigurationService(ICurrentUser user) { CurrentUser = user; }

    public string BuildConnectionString() {
        return string.Format(DefaultConnectionString
            , CurrentUser.DatabaseInstanceName
            , CurrentUser.Login
            , CurrentUser.Password);
    }

    private readonly ICurrentUser CurrentUser;
}

public class CurrentUser : ICurrentUser {
    public CurrentUser(string dbinstance, string login, string password) {
        DatabaseInstanceName = dbinstance;
        Login = login;
        Passwword = password;
    }

    public readonly string DatabaseInstanceName;
    public readonly string Login;
    public readonly string Password;
}

string dbInstance = authenticationDialog.DatabaseInstanceName;
string login = authenticationDialog.Login;
string password = authenticationDialog.Password;

var nHibernateConfigurationProvider =
    new ConfigurationProvider(
        new ConfigurationService(
            new CurrentUser(dbInstance, login, password)).BuildConnectionString()
        , Assembly.GetExecutingAssembly());

// Wait until user is authenticated before continuing to bind???
Bind<string>().ToMethod(ctx => ctx.Request.???.BuildConnectionString()).WhenInjectedInto<ConfigurationProvider>().InSingletonScope();
Bind<Assembly>().ToConstant<Assembly>(Assembly.GetExecutingAssembly().WhenInjectedInto<ConfigurationProvider>();

// Do your stuff to collect credentials

// User now authenticated, initialize ICurrentUser instance singleton
// You could have used a ICurrentUserFactory or static member, this is just a sample implementation
kernel.Get<ICurrentUser>(new ConstructorArgument("dbInstance", dbInstance),
    new ConstructorArgument("login", login),
    new ConstructorArgument("password", password));

// You can now access your NHibernate configuration properly
var config = kernel.Get<Configuration>();

Bind<Configuration>().ToProvider<ConfigurationProvider>();
Bind<ConfigurationProvider>()
    .ToMethod(
        ctx => new ConfigurationProvider(ctx.Kernel.Get<ConfigurationService>().BuildConnectionString()));

Bind<ICurrentUser>().To<CurrentUser>().InSingletonScope();