Your best bet would be to use a power bank, which contains a lithium ion battery, and charging and protections circuits already built in. And they are for sale for cheaper than you could make the equivalent.
The key to sizing it is Watt Hours. A battery pack is rated in Amp hour, or more likely milliamp hours. Typical ones will have something like 10000 mA Hours which is 10 Amp Hours. You need to convert that to Watt hours. That is simply the Amp Hours multiplied by the voltage. So, if you have a 5V, 10000mAH power bank (a common size) that is 50 Watt Hours.
Now you need to know how much power your bluetooth speakers will use in Watts (combined). Then, to estimate the life of the batteries between charges, you simply divide the Watt Hours of the battery pack by the Watts consumed by the speakers.
Say each speaker consumes 3W. Note that this is not the audio output of the speaker, but the power consumption, which can be twice the audio output. So if each speaker consumes 3W then you have 9W of total consumption. Your 50 Watt Hour battery pack would then last 50 / 9 = 5.6 Hours.
For the best run time, you want to use class D amplifiers, which are over 90% efficient, as opposed to the older style of class AB amplifiers which are less than 50% efficient.
There are little class D stereo amplifier available very cheap on Ebay that run off 5V (which is the most common voltage you will find a on power bank) and can output about 2W audio per channel. This would probably be a good choice. If all three speakers were stereo and outputting using about 5W (2W per channel plus some loss), your total consumption would be 15W and run time off a 10000mAH battery pack would be a little over 3 hours.
Now for the disclaimer. The capacity rating of the power banks are typically overstated by quite a bit. For one thing, they might be quoting the maH at the battery, which is 3.7V as opposed to the output which is 5V. This means you would have to multiply by 3.7 instead of 5 to get the Watt hours. So your 10000mAH power bank might really be 37 Watt hours instead of 50 Watt hours. And that is if they are giving a realistic number for the capacity at the battery level.
Bob