Yes, there is a better alternative to either of these. That alternative is a little bit of politeness! Whilst it might be acceptable in Russian to bark 'Check please!' at a waiter, this would not go down well in either New York or London. You would get a very rude reaction from any restaurant owner or waiter you addressed in this way in English-speaking countries. 'Can we get the check, please?' (US) or 'Can we have the bill, please?' (GB) is the minimum of courtesy required.

Hi Julia, "Check" is used in the US and "Bill" is used in the UK, both are correct.

"Check please" is a little bit brusque. I usually say "Can we get the check, please?"