How to open/close react-bootstrap modal programmatically?

What you are looking for is the custom modal trigger, which uses the OverlayMixin and allows you to manage the modal's state yourself. You can control whether the modal is shown using this.setState({isModalOpen: true}) to achieve the equivalent of what you asked for in your post in the example below. The following code is from the react-bootstrap website (http://react-bootstrap.github.io/components.html#modals):

const CustomModalTrigger = React.createClass({
  mixins: [OverlayMixin],

  getInitialState() {
    return {
      isModalOpen: false
    };
  },

  handleToggle() {
    this.setState({
      isModalOpen: !this.state.isModalOpen
    });
  },

  render() {
    return (
      <Button onClick={this.handleToggle} bsStyle='primary'>Launch</Button>
    );
  },

  // This is called by the `OverlayMixin` when this component
  // is mounted or updated and the return value is appended to the body.
  renderOverlay() {
    if (!this.state.isModalOpen) {
      return <span/>;
    }

    return (
      <Modal bsStyle='primary' title='Modal heading' onRequestHide={this.handleToggle}>
        <div className='modal-body'>
          This modal is controlled by our custom trigger component.
        </div>
        <div className='modal-footer'>
          <Button onClick={this.handleToggle}>Close</Button>
        </div>
      </Modal>
    );
  }
});

React.render(<CustomModalTrigger />, mountNode);

UPDATE (Aug 4, 2015)

In the newest version of React-Bootstrap, whether a modal is shown or not is controlled by a show prop which is passed to the modal. The OverlayMixin is no longer needed to control the modal state. Controlling the state of the modal is still done via setState, in this example via this.setState({ showModal: true }). The following is based off the example on the React-Bootstrap website:

const ControlledModalExample = React.createClass({

  getInitialState(){
    return { showModal: false };
  },

  close(){
    this.setState({ showModal: false });
  },

  open(){
    this.setState({ showModal: true });
  },

  render() {
    return (
      <div>
        <Button onClick={this.open}>
          Launch modal
        </Button>

        <Modal show={this.state.showModal} onHide={this.close}>
          <Modal.Header closeButton>
            <Modal.Title>Modal heading</Modal.Title>
          </Modal.Header>
          <Modal.Body>
            <div>Modal content here </div>
          </Modal.Body>
          <Modal.Footer>
            <Button onClick={this.close}>Close</Button>
          </Modal.Footer>
        </Modal>
      </div>
    );
  }
});

You can do it with React hooks. (Included in React 16.8)

import React, { useState } from "react";
import { Modal, Button } from "react-bootstrap";

const ComponentWithModal = props => {
  const [isModalOpen, setModalStatus] = useState(false);

  return (
    <div>
      <div>I am a Bootstrap Modal</div>
      <Button onClick={() => setModalStatus(true)}>Show Modal</Button>
      <div>
        <Modal
          className="modal-container"
          show={isModalOpen}
          onHide={() => setModalStatus(false)}
        >
          <Modal.Header closeButton>
            <Modal.Title>Modal title</Modal.Title>
          </Modal.Header>

          <Modal.Body>Modal content here</Modal.Body>

          <Modal.Footer>
            <Button onClick={() => setModalStatus(false)}>Close</Button>
          </Modal.Footer>
        </Modal>
      </div>
    </div>
  );
};

export default ComponentWithModal;

Your modal will have a show prop and an onHide prop to determine when it's displayed. E.g.:

<Modal show={this.state.showModal} onHide={this.close}>

The onHide function simply changes showModal state property. Your modal is shown/hidden based on the parent's state:

close(){
  this.setState({ showModal: false });
}

If you'd like to close the modal from within the modal itself, you can trigger the onHide function defined on the parent via props. For example, this is a button somewhere inside the modal closing it:

<button type="button" className="close" onClick={this.props.onHide}>
  <span>&times;</span>
</button>

Here is a fiddle simulating this workflow.

Open and close react-bootstrap modal programmatically/dynamically from the state:

Here I used the ES6 syntax class component syntax.

import React, { Component, PropTypes } from 'react';
import { Modal, Button } from 'react-bootstrap';
import './GenericModal.scss';

class GenericModal extends Component {
  constructor(props, context) {
  super(props, context);

  this.state = {
    showModal: false
  };

  this.open = this.open.bind(this);
  this.close = this.close.bind(this);
}


open() {
  this.setState({showModal: true});
}

close() {
  this.setState({showModal: false});
}

render() {
  return(
    <div>
      <div>I am a Bootstrap Modal</div>
      <Button onClick={this.open}>Show Modal</Button>
      <div>
        <Modal className="modal-container" 
          show={this.state.showModal} 
          onHide={this.close}
          animation={true} 
          bsSize="small">

          <Modal.Header closeButton>
            <Modal.Title>Modal title</Modal.Title>
          </Modal.Header>

          <Modal.Body>
            One of fine body.........
          </Modal.Body>

          <Modal.Footer>
            <Button onClick={this.close}>Close</Button>
            <Button bsStyle="primary">Save changes</Button>
          </Modal.Footer>         
        </Modal> 
      </div>
    </div>
  );
 }
}

export default GenericModal;