I am using Twitter Bootstrap and I want to use an \"auto-suggest\" which is not available in Bootstrap, whereas jQuery UI has its own methods for auto-suggest.
Can I
Yes you can use both. js bootstrap from twitter is a collection of jquery plugins. There shohuldn't be any conflict with jQuery UI.
Regarding bandwidth overload, it really depends on how you handle the requests to load all of your js files. if you really dont want to make multiple requests to the server to request for each file, just append them together and minimize. Or you probably can get rid of some js bootstrap plugins you dont need. it is very modular.