You can certainly pay by your credit card when you place your sports bets but a better system known as a web wallet system is Moneybookers as it is far superior to using credit cards and is super quick.
As credit card transactions take place only through secure servers it is certainly safe than when you use it in any store or even in any restaurant. Credit cards are simply superior to bank transfers. If any bookmaker cheats you then you at least have a chance to get compensated by the credit card company.
Visa has the highest acceptance by bookmakers with the next highest being MasterCard and credit card companies usually assist card holders if they face any problem.
MasterCard can get you bonuses whenever you play. Also, even as you play on Sure Bets (bet arbs) and never lose your bet, you can have large amounts of money to spread between various bookmakers and this in effect is also a bonus.