ExpandingTextInput.js

var React = require('react-native')
var {
  TextInput
} = React;

var RCTUIManager   = require('NativeModules').UIManager;
var findNodeHandle = require('findNodeHandle');

var ExpandingTextInput = React.createClass({
  propTypes: React.TextInput.propTypes,

  getInitialState: function() {
    return {
      height: 50
    };
  },

  setNativeProps: function(nativeProps) {
    var input  = this.refs.input;
    input.setNativeProps(nativeProps);

    if (nativeProps.text !== undefined) {
      this.resetHeight();
    }
  },

  onMeasureTextHeight: function(height) {
    if (this.isMounted()) {
      // console.log("onMeasureTextHeight: " + height);

      // it's not clear to me why this is needed but it seems to help
      // the height looks good at 50 and Xcode says it's 38
      height += 12;

      if (height < 50)  height = 50;
      if (height > 120) height = 120;

      if (this.state.height !== height) {
        this.setState({height: height});
      }
    }
  },

  resetHeight: function() {
    RCTUIManager.measureTextHeight(
      findNodeHandle(this.refs.input.refs.input),
      this.onMeasureTextHeight
    );
  },

  onChange: function(event) {
    //console.log('ExpandingTextInput.onChange');
    this.resetHeight();
    if (this.props.onChange) this.props.onChange(event);
  },

  render: function() {
    var passedStyle = this.props.style || {};
    return (
      <TextInput
        {...this.props}
        placeholder={"Enter message"}
        onChange={this.onChange}
        multiline={true}
        ref="input"
        style={[styles.input, passedStyle, {height: this.state.height}]}
      />
    );
  }
});

var styles = StyleSheet.create({
  input: {
    padding: 10,
    flex: 1,
    fontSize: 18
  }
});

module.exports = ExpandingTextInput;

RCTUIManager+TextView.m

//
//  RCTUIManager+TextView.m
//  Tasker
//
//  Created by Brian Leonard on 7/31/15.
//

#import <UIKit/UIKit.h>
#import "RCTUIManager.h"
#import "RCTSparseArray.h"
#import "UIView+React.h"


@interface RCTUIManager (TextView)

@end

@implementation RCTUIManager (TextView)

/**
 * Returns information about the content inside of a RCTTextView
 */
RCT_EXPORT_METHOD(measureTextHeight:(NSNumber *)reactTag
                  callback:(RCTResponseSenderBlock)callback)
{
  if (!callback) {
    RCTLogError(@"Called measure with no callback");
    return;
  }
  
  [self addUIBlock:^(__unused RCTUIManager *uiManager, RCTSparseArray *viewRegistry) {
    UIView *view = viewRegistry[reactTag];
    if (!view) {
      RCTLogError(@"measureTextContent cannot find view with tag #%@", reactTag);
      return;
    }

    UIView *rootView = view;
    while (rootView && ![rootView isReactRootView]) {
      rootView = rootView.superview;
    }
    
    UITextView *textView = nil;
    NSArray *subviews = [view subviews];
    
    for(UIView *subview in subviews) {
      if ([subview isKindOfClass:[UITextView class]]) {
        UITextView * test = (UITextView *)subview;
        if (![test isHidden]) { // placeholder is hidden
          textView = test;
          break;
        }
      }
    }
    
    if (!textView) {
      RCTLogError(@"measureTextContent cannot find UITextView from tag #%@", reactTag);
      return;
    }
    
    // http://stackoverflow.com/questions/19046969/uitextview-content-size-different-in-ios7
    CGFloat measuredHeight;
    if (floor(NSFoundationVersionNumber) > NSFoundationVersionNumber_iOS_6_1)
    {
      // This is the code for iOS 7. contentSize no longer returns the correct value, so
      // we have to calculate it.
      //
      // This is partly borrowed from HPGrowingTextView, but I've replaced the
      // magic fudge factors with the calculated values (having worked out where
      // they came from)
      
      CGRect frame = textView.bounds;
      
      // Take account of the padding added around the text.
      
      UIEdgeInsets textContainerInsets = textView.textContainerInset;
      UIEdgeInsets contentInsets = textView.contentInset;
      
      CGFloat leftRightPadding = textContainerInsets.left + textContainerInsets.right + textView.textContainer.lineFragmentPadding * 2 + contentInsets.left + contentInsets.right;
      CGFloat topBottomPadding = textContainerInsets.top + textContainerInsets.bottom + contentInsets.top + contentInsets.bottom;
      
      frame.size.width -= leftRightPadding;
      frame.size.height -= topBottomPadding;
      
      NSString *textToMeasure = textView.text;
      if ([textToMeasure hasSuffix:@"\n"])
      {
        textToMeasure = [NSString stringWithFormat:@"%@-", textView.text];
      }
      
      // NSString class method: boundingRectWithSize:options:attributes:context is
      // available only on ios7.0 sdk.
      
      NSMutableParagraphStyle *paragraphStyle = [[NSMutableParagraphStyle alloc] init];
      [paragraphStyle setLineBreakMode:NSLineBreakByWordWrapping];
      
      NSDictionary *attributes = @{ NSFontAttributeName: textView.font, NSParagraphStyleAttributeName : paragraphStyle };
      
      CGRect size = [textToMeasure boundingRectWithSize:CGSizeMake(CGRectGetWidth(frame), MAXFLOAT)
                                                options:NSStringDrawingUsesLineFragmentOrigin
                                             attributes:attributes
                                                context:nil];
      
      measuredHeight = ceilf(CGRectGetHeight(size) + topBottomPadding);
    }
    else
    {
      measuredHeight = textView.contentSize.height;
    }

    callback(@[ @(measuredHeight) ]);
  }];
}

@end

Do you mind if I ask how to install this? I've never created a bridge module before and all my attempts to add this .m file have not worked. Thanks!