Hide function is not a public function on OverlayTrigger. Set <OverlayTrigger rootClose={true}... and then on your onClick event trigger call document.body.click().

I was facing the same problem I thought the cleanest way to solve it is to use a conditional wrapper.

const ConditionalWrapper = ({
    condition,
    wrapper,
    children,
}) => (condition ? wrapper(children) : children);


export class NextButton extends React.Component {
    render () {
        return (
            <div>
                <ConditionalWrapper
                    condition={this.props.someCondition}
                    wrapper={children => (
                        <OverlayTrigger
                            overlay={<Popover>Please enter a title.</Popover>}
                            placement='top'
                        >
                            {children}
                        </OverlayTrigger>
                        )}
                >
                    {/* wrap this in a div so when the button is disabled, the popover still works */}
                    <div>
                        <Button
                            onClick={() => this.props.goToNextPage()}
                            disabled={this.props.someCondition}
                        >
                            Next
                        </Button>
                    </div>
                </ConditionalWrapper>
            </div>
        );
    }
}

The default behaviour of the trigger prop of OverlayTrigger is ['hover', 'focus'] so the tooltip will display both when hovered over and focussed on.

To change this so that you only get the tooltip on hover you can set the value of trigger to ['hover']:

<OverlayTrigger
  ...
  trigger={["hover"]}
>
  <Button onClick={handleOpenModal}>Open Modal</Button>
</OverlayTrigger>

There's a working demo here - when the close the modal the button still has focus, but the tooltip is not displayed unless you hover your mouse over the button.