You can set an id to the form and reference it by the form attribute of the button:
<ion-view title="Title">
<ion-nav-buttons side="right">
<button type="submit" form="myForm">
</ion-nav-buttons>
<ion-header-bar>
</ion-header-bar>
<ion-content>
<form id="myForm">
<input name="myFormInput">
</form>
</ion-content>
</ion-view>