When a graduate college is lucky enough to attract competent creative postgraduate students, there is a mechanism, that I have learnt during my studies at Bradford University (England), which can bridge the gap between postgraduate & undergraduate research studies. I have been involved in this mechanism.
The postgraduate student will be surely concerned with a variety of topics. This student will be asked by his/her supervisor to suggest few research ideas for undergrad. students to choose from. Once a student decides to undertake a certain research idea, s/he will be directed to keep in touch with the supervisor & the postgraduate student.
This triangular relationship will benefit all the participants. If the undergrad. student shows capability & enthusiasm , then the postgraduate student (as a first "contactor") will try to win him/her to continue research in further relevant projects and will give recommendation for that. This way, the undergrad. student will climb the ladder in a "natural" way.
What I have seen working well is when a Professor includes undergraduate students in his/her research team that already has experienced researchers and PhD candidates. The undergraduates seamlessly transition into graduate work with enthusiasm, especially if they had enjoyed some benefits as "researchers," e.g. being included as co-authors in some of the Professor's publications