Question: how do I connect to each other with lan without data or internet on minecraft pocket edition can I use Bluetooth or is there any bugs?

Answer: 
Wireless
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Yes, a wireless router will be enough for playing MC PE (even if the router doesn't have Internet connection). Just go to settings in MC PE while playing in a world, select multiplayer and enable both sliders (Multiplayer game and visible to LAN players.)

A way connect without using a router: (Doesn't work on iPad)

Turn on personal hotspot and turn on Wi-Fi on the device which has the world you want to connect (It's called "host"), now you should choose that device from Wi-Fi network list in device settings from the other device.

Bluetooth
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Currently MC PE doesn't support Bluetooth multiplayer officially, but there are tricks to do that.

Option 1: (The host must be an iOS (Apple) device.)

Download [Multiplayer for Minecraft PE](https://appsto.re/i6dX7fD) (Paid), set up your server and turn on Bluetooth.

Option 2: (The host mustn't be an iPad.)

Turn on personal hotspot and turn on Bluetooth, your friend should choose your device from bluetooth device list in device settings.

Here's how to enable personal hotspot on [Apple devices](https://support.apple.com/en-us/HT204023) and [Android devices](http://www.dummies.com/consumer-electronics/smartphones/droid/how-to-create-a-mobile-hotspot-with-an-android-phone/).

Last step to do
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If you did one of these, your friend should see your world on world list like this:

![](https://winblogs.azureedge.net/devices/2015/09/Minecraft_Pocket-Edition_Join-game.jpg)

Image source: <https://blogs.windows.com/devices/2015/09/18/how-to-play-multiplayer-minecraft-pocket-edition/>
A lan can be many things, multiple devices on a router for example.
But lan is more defined as computing devices that communicate.

You can achieve this by connecting two computers with a lan cable, no router required.

You can make a lan using Bluetooth, or just a phone hotspot.

You can even make a lan using one pc. You can run a program that runs two separate versions of 64bit Windows that can communicate to eachothers and render it in split screen. 
(Similar but not quite what console split screen does) 

All from the same pc...

This guy, In the comments, you can tell he doesn't know what he's doing.
The devices need some means of communication, they are not magic.
The comment was not well worded but I did my best to decipher your text.
If it's a Xbox you are going to want to connect to her phone's hotspot. 

She will by default have the same ip, because your just a extention of her phone's data.

I am not sure how it works on Xbox, but Xbox might require you to login.