This customization is only for the Booking Calendar Free version. In the paid versions, you can easily configure booking form fields and their style at the advanced form configuration at the Booking > Settings > Fields page.

Customization.
1) Please add this CSS to your Theme Editor settings. You can check how to add own CSS customization to CSS Theme Editor here.

Here's the CSS code you need to add to set the Labels (text near input fields) color as white:

.booking_form .control-label {
  color: #FFF;
}

Of course instead of white color #FFF you can set some other color. For black labels, please use #000 insteaf of #fff.

Please do not forget to clear the browser cache before testing these changes.

2) In the same way possible to change the color of text inside of the text fields, text-area elements and select-boxes.

CSS for setting text color as white

.booking_form_div select,
.booking_form_div textarea,
.booking_form_div input[type="text"],
.booking_form_div input[type="email"] {
  color: #FFF;
}

CSS for setting text color as black:

.booking_form_div select,
.booking_form_div textarea,
.booking_form_div input[type="text"],
.booking_form_div input[type="email"] {
  color: #000;
}

Important! Please note after update of plugin to the newer version update, you will be need to make this fix again, because all Booking Calendar files will be overwritten.

3) In case if you need to update the colors of the buttons in the booking form, please use the CSS similar to this:

.wpbc_container .wpbc_button_light, 
.wpbc_container.wpbc_container_booking_form .wpbc_button_light {
	box-shadow: none !important;
	border: 0 !important;
	border-radius: 0 !important;
	background-color: #B78F60 !important;
	color: #fff !important;
}
.wpbc_container .wpbc_button_light:hover,
.wpbc_container .wpbc_button_light:focus {
	background-color: #3C3C3B !important;
}