"busy participating" is correct and usable in written English.
It is typically used when someone is occupied by taking part in an activity or event. Example: She has been busy participating in online painting classes.
Herb and Dorothy are no longer collecting, and are now busy participating in each museum's inaugural exhibition of the collection.
IN AN intriguing exchange a few days ago, Dani Rodrik expressed his faith in the Costa Rican people, who were busy participating in referendum on whether or not that nation ought to participate in the CAFTA regional trade agreement.
In the evenings, they are busy participating in various programs, including the crochet club, whose members make and donate mittens, scarves and lapghans to nearby charitable groups each winter.
Boss professors are busy participating in conferences, developing guanxi, and grabbing projects and funds, while young investigators have to practically fulfill these projects and write papers with the names of the boss professors in the author list, sometimes as the first author, even if the boss professors do not know what was written in the paper.
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When she's not busy participating in hyper-colorful Japanese environmental TV shows or lodged in an East London office brainstorming on the future of the future, 32-year-old Ai Hasegawa's concerns are no different than those of any woman her age: the relentless tick-tick-ticking of her biological clock.
In mid-January, a smaller set of interviewers attempted to schedule interviews with participants who were previously too busy to participate.
Nevertheless, other potential biasing factors which might have resulted in low response rate should also be taken into account; for instance, the non-responders might not be interested in EIDM, might not consider it relevant to their practice, might not see the importance of participation, or simply might be too busy to participate.
Many of the non-participants indicated (verbally or in writing) they were "too busy" to participate.
What is interesting in this debate is that highly skilled people who are often too busy to participate in local politics have taken time to get involved.
One round table participant, who is in charge of a mentoring program, said her female mentees were unreliable and not ready to be mentored since they had other priorities (family obligations), so they tended to cancel their appointments, were too busy to participate, etc.
