How can I set elevation shadow only on the bottom on react native?

You can use overflow: 'hidden' to achieve the desired result without having to install a library.
wrap the view in a parent view and set the parent's overflow to hidden and apply a padding only on the side where you want your shadow to appear like so:

  <View style={{ overflow: 'hidden', paddingBottom: 5 }}>
    <View
      style={{
        backgroundColor: '#fff',
        width: 300,
        height: 60,
        shadowColor: '#000',
        shadowOffset: { width: 1, height: 1 },
        shadowOpacity:  0.4,
        shadowRadius: 3,
        elevation: 5,
      }} 
    />
  </View>

result:

here's a custom component that you can use:

import React from 'react'
import { View, StyleSheet, ViewPropTypes } from 'react-native'
import PropTypes from 'prop-types'


const SingleSidedShadowBox = ({ children, style }) => (
  <View style={[ styles.container, style ]}>
    { children }
  </View>
);

const styles = StyleSheet.create({
  container:{
    overflow: 'hidden',
    paddingBottom: 5,
  }
});

SingleSidedShadowBox.propTypes = {
  children: PropTypes.element,
  style: ViewPropTypes.style,
};

export default SingleSidedShadowBox;

example:

<SingleSidedShadowBox style={{width: '90%', height: 40}}>
  <View style={{
    backgroundColor: '#fff',
    width: '100%',
    height: '100%',
    shadowColor: '#000',
    shadowOffset: { width: 1, height: 1 },
    shadowOpacity:  0.4,
    shadowRadius: 3,
    elevation: 5,
  }} />
</SingleSidedShadowBox>

you can adjust the padding depending on your shadow

Unfortunately RN don't support it by default, check blow link https://ethercreative.github.io/react-native-shadow-generator/

but you can use npm packages like this